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Hermann Weyl - Wikipedija, prosta enciklopedija
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mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Strani za neprijavljene urejevalce <a href="/wiki/Pomo%C4%8D:Uvod" aria-label="Več o urejanju"><span>več o tem</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Posebno:MojiPrispevki" title="Seznam urejanj s tega IP-naslova [y]" accesskey="y"><span>Prispevki</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Posebno:MojPogovor" title="Pogovor o urejanjih s tega IP-naslova [n]" accesskey="n"><span>Pogovorna stran</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><!-- CentralNotice --></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" 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data-event-name="pinnable-header.vector-toc.unpin">skrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Uvod</div> </a> </li> <li id="toc-Življenje_in_delo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Življenje_in_delo"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Življenje in delo</span> </div> </a> <button aria-controls="toc-Življenje_in_delo-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vklopi podrazdelek Življenje in delo</span> </button> <ul id="toc-Življenje_in_delo-sublist" class="vector-toc-list"> <li id="toc-Geometrijski_temelji_mnogoterosti_in_fizike" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geometrijski_temelji_mnogoterosti_in_fizike"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Geometrijski temelji mnogoterosti in fizike</span> </div> </a> <ul id="toc-Geometrijski_temelji_mnogoterosti_in_fizike-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Temelji_matematike" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temelji_matematike"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Temelji matematike</span> </div> </a> <ul id="toc-Temelji_matematike-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Glavna_dela" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Glavna_dela"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Glavna dela</span> </div> </a> <ul id="toc-Glavna_dela-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Priznanja" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Priznanja"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Priznanja</span> </div> </a> <button aria-controls="toc-Priznanja-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vklopi podrazdelek Priznanja</span> </button> <ul id="toc-Priznanja-sublist" class="vector-toc-list"> <li id="toc-Nagrade" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nagrade"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Nagrade</span> </div> </a> <ul id="toc-Nagrade-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Poimenovanja" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Poimenovanja"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Poimenovanja</span> </div> </a> <ul id="toc-Poimenovanja-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sklici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sklici"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Sklici</span> </div> </a> <ul id="toc-Sklici-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Viri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Viri"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Viri</span> </div> </a> <ul id="toc-Viri-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zunanje_povezave" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zunanje_povezave"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Zunanje povezave</span> </div> </a> <ul id="toc-Zunanje_povezave-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Vsebina" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Vklopi kazalo vsebine" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vklopi kazalo vsebine</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Hermann Weyl</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="P9jdi na članek v drugem jeziku. Na voljo v 60 jezikih." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-60" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">60 jezikov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%8A%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D8%A7%D9%8A%D9%84" title="هيرمان فايل – arabščina" lang="ar" hreflang="ar" data-title="هيرمان فايل" data-language-autonym="العربية" data-language-local-name="arabščina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%87%D9%8A%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D8%A7%D9%8A%D9%84" title="هيرمان فايل – Egyptian Arabic" lang="arz" hreflang="arz" data-title="هيرمان فايل" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – asturijščina" lang="ast" hreflang="ast" data-title="Hermann Weyl" data-language-autonym="Asturianu" data-language-local-name="asturijščina" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Herman_Veyl" title="Herman Veyl – azerbajdžanščina" lang="az" hreflang="az" data-title="Herman Veyl" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanščina" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%88%DB%8C%D9%84" title="هرمان ویل – South Azerbaijani" lang="azb" hreflang="azb" data-title="هرمان ویل" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB%D1%8C" title="Герман Вейль – beloruščina" lang="be" hreflang="be" data-title="Герман Вейль" data-language-autonym="Беларуская" data-language-local-name="beloruščina" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B0%D0%B9%D0%BB" title="Херман Вайл – bolgarščina" lang="bg" hreflang="bg" data-title="Херман Вайл" data-language-autonym="Български" data-language-local-name="bolgarščina" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A7%87%E0%A6%B0%E0%A7%8D%E0%A6%AE%E0%A6%BE%E0%A6%A8_%E0%A6%AD%E0%A6%BE%E0%A6%87%E0%A6%B2" title="হের্মান ভাইল – bengalščina" lang="bn" hreflang="bn" data-title="হের্মান ভাইল" data-language-autonym="বাংলা" data-language-local-name="bengalščina" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – bosanščina" lang="bs" hreflang="bs" data-title="Hermann Weyl" data-language-autonym="Bosanski" data-language-local-name="bosanščina" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – katalonščina" lang="ca" hreflang="ca" data-title="Hermann Weyl" data-language-autonym="Català" data-language-local-name="katalonščina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – češčina" lang="cs" hreflang="cs" data-title="Hermann Weyl" data-language-autonym="Čeština" data-language-local-name="češčina" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – danščina" lang="da" hreflang="da" data-title="Hermann Weyl" data-language-autonym="Dansk" data-language-local-name="danščina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – nemščina" lang="de" hreflang="de" data-title="Hermann Weyl" data-language-autonym="Deutsch" data-language-local-name="nemščina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%AD%CF%81%CE%BC%CE%B1%CE%BD_%CE%92%CE%AC%CF%85%CE%BB" title="Χέρμαν Βάυλ – grščina" lang="el" hreflang="el" data-title="Χέρμαν Βάυλ" data-language-autonym="Ελληνικά" data-language-local-name="grščina" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – angleščina" lang="en" hreflang="en" data-title="Hermann Weyl" data-language-autonym="English" data-language-local-name="angleščina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – esperanto" lang="eo" hreflang="eo" data-title="Hermann Weyl" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – španščina" lang="es" hreflang="es" data-title="Hermann Weyl" data-language-autonym="Español" data-language-local-name="španščina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – estonščina" lang="et" hreflang="et" data-title="Hermann Weyl" data-language-autonym="Eesti" data-language-local-name="estonščina" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – baskovščina" lang="eu" hreflang="eu" data-title="Hermann Weyl" data-language-autonym="Euskara" data-language-local-name="baskovščina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%88%D8%A7%DB%8C%D9%84" title="هرمان وایل – perzijščina" lang="fa" hreflang="fa" data-title="هرمان وایل" data-language-autonym="فارسی" data-language-local-name="perzijščina" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – finščina" lang="fi" hreflang="fi" data-title="Hermann Weyl" data-language-autonym="Suomi" data-language-local-name="finščina" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – francoščina" lang="fr" hreflang="fr" data-title="Hermann Weyl" data-language-autonym="Français" data-language-local-name="francoščina" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – irščina" lang="ga" hreflang="ga" data-title="Hermann Weyl" data-language-autonym="Gaeilge" data-language-local-name="irščina" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – galicijščina" lang="gl" hreflang="gl" data-title="Hermann Weyl" data-language-autonym="Galego" data-language-local-name="galicijščina" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A8%D7%9E%D7%9F_%D7%95%D7%99%D7%99%D7%9C" title="הרמן וייל – hebrejščina" lang="he" hreflang="he" data-title="הרמן וייל" data-language-autonym="עברית" data-language-local-name="hebrejščina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – haitijska kreolščina" lang="ht" hreflang="ht" data-title="Hermann Weyl" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitijska kreolščina" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – madžarščina" lang="hu" hreflang="hu" data-title="Hermann Weyl" data-language-autonym="Magyar" data-language-local-name="madžarščina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D6%80%D5%B4%D5%A1%D5%B6_%D5%8E%D5%A5%D5%B5%D5%AC" title="Հերման Վեյլ – armenščina" lang="hy" hreflang="hy" data-title="Հերման Վեյլ" data-language-autonym="Հայերեն" data-language-local-name="armenščina" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – indonezijščina" lang="id" hreflang="id" data-title="Hermann Weyl" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijščina" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – italijanščina" lang="it" hreflang="it" data-title="Hermann Weyl" data-language-autonym="Italiano" data-language-local-name="italijanščina" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%98%E3%83%AB%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AF%E3%82%A4%E3%83%AB" title="ヘルマン・ワイル – japonščina" lang="ja" hreflang="ja" data-title="ヘルマン・ワイル" data-language-autonym="日本語" data-language-local-name="japonščina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%97%A4%EB%A5%B4%EB%A7%8C_%EB%B0%94%EC%9D%BC" title="헤르만 바일 – korejščina" lang="ko" hreflang="ko" data-title="헤르만 바일" data-language-autonym="한국어" data-language-local-name="korejščina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – kurdščina" lang="ku" hreflang="ku" data-title="Hermann Weyl" data-language-autonym="Kurdî" data-language-local-name="kurdščina" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB" title="Герман Вейл – kirgiščina" lang="ky" hreflang="ky" data-title="Герман Вейл" data-language-autonym="Кыргызча" data-language-local-name="kirgiščina" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – litovščina" lang="lt" hreflang="lt" data-title="Hermann Weyl" data-language-autonym="Lietuvių" data-language-local-name="litovščina" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Hermanis_Veils" title="Hermanis Veils – latvijščina" lang="lv" hreflang="lv" data-title="Hermanis Veils" data-language-autonym="Latviešu" data-language-local-name="latvijščina" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – malgaščina" lang="mg" hreflang="mg" data-title="Hermann Weyl" data-language-autonym="Malagasy" data-language-local-name="malgaščina" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B0%D1%98%D0%BB" title="Херман Вајл – makedonščina" lang="mk" hreflang="mk" data-title="Херман Вајл" data-language-autonym="Македонски" data-language-local-name="makedonščina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9F%E1%80%AC%E1%80%99%E1%80%94%E1%80%BA_%E1%80%97%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9C%E1%80%BA" title="ဟာမန် ဗိုင်းလ် – burmanščina" lang="my" hreflang="my" data-title="ဟာမန် ဗိုင်းလ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmanščina" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – nizozemščina" lang="nl" hreflang="nl" data-title="Hermann Weyl" data-language-autonym="Nederlands" data-language-local-name="nizozemščina" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – novonorveščina" lang="nn" hreflang="nn" data-title="Hermann Weyl" data-language-autonym="Norsk nynorsk" data-language-local-name="novonorveščina" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Claus_Hugo_Hermann_Weyl" title="Claus Hugo Hermann Weyl – knjižna norveščina" lang="nb" hreflang="nb" data-title="Claus Hugo Hermann Weyl" data-language-autonym="Norsk bokmål" data-language-local-name="knjižna norveščina" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – poljščina" lang="pl" hreflang="pl" data-title="Hermann Weyl" data-language-autonym="Polski" data-language-local-name="poljščina" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Piedmontese" lang="pms" hreflang="pms" data-title="Hermann Weyl" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – portugalščina" lang="pt" hreflang="pt" data-title="Hermann Weyl" data-language-autonym="Português" data-language-local-name="portugalščina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B5%D0%B9%D0%BB%D1%8C,_%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD" title="Вейль, Герман – ruščina" lang="ru" hreflang="ru" data-title="Вейль, Герман" data-language-autonym="Русский" data-language-local-name="ruščina" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – sicilijanščina" lang="scn" hreflang="scn" data-title="Hermann Weyl" data-language-autonym="Sicilianu" data-language-local-name="sicilijanščina" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – srbohrvaščina" lang="sh" hreflang="sh" data-title="Hermann Weyl" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbohrvaščina" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hermann Weyl" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B0%D1%98%D0%BB" title="Херман Вајл – srbščina" lang="sr" hreflang="sr" data-title="Херман Вајл" data-language-autonym="Српски / srpski" data-language-local-name="srbščina" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – švedščina" lang="sv" hreflang="sv" data-title="Hermann Weyl" data-language-autonym="Svenska" data-language-local-name="švedščina" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB" title="Герман Вейл – tadžiščina" lang="tg" hreflang="tg" data-title="Герман Вейл" data-language-autonym="Тоҷикӣ" data-language-local-name="tadžiščina" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – turščina" lang="tr" hreflang="tr" data-title="Hermann Weyl" data-language-autonym="Türkçe" data-language-local-name="turščina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Wayl_Hermann" title="Wayl Hermann – tatarščina" lang="tt" hreflang="tt" data-title="Wayl Hermann" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarščina" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB%D1%8C" title="Герман Вейль – ukrajinščina" lang="uk" hreflang="uk" data-title="Герман Вейль" data-language-autonym="Українська" data-language-local-name="ukrajinščina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – uzbeščina" lang="uz" hreflang="uz" data-title="Hermann Weyl" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeščina" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – vietnamščina" lang="vi" hreflang="vi" data-title="Hermann Weyl" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamščina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%B0%E1%83%94%E1%83%A0%E1%83%9B%E1%83%90%E1%83%9C_%E1%83%95%E1%83%90%E1%83%98%E1%83%9A%E1%83%98" title="ჰერმან ვაილი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჰერმან ვაილი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E5%A4%96%E5%B0%94" title="赫尔曼·外尔 – kitajščina" lang="zh" hreflang="zh" data-title="赫尔曼·外尔" data-language-autonym="中文" data-language-local-name="kitajščina" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%B5%AB%E7%88%BE%E6%9B%BC%C2%B7%E5%A4%96%E7%88%BE" title="赫爾曼·外爾 – kantonščina" lang="yue" hreflang="yue" data-title="赫爾曼·外爾" data-language-autonym="粵語" data-language-local-name="kantonščina" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q71029#sitelinks-wikipedia" title="Uredi medjezikovne povezave" class="wbc-editpage">Uredi povezave</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Hermann_Weyl" title="Ogled vsebinske strani [c]" accesskey="c"><span>Stran</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Pogovor:Hermann_Weyl" rel="discussion" title="Pogovor o vsebinski strani [t]" accesskey="t"><span>Pogovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Spremeni različico jezika" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">slovenščina</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Hermann_Weyl"><span>Preberi</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&action=history" title="Prejšnje redakcije te strani [h]" accesskey="h"><span>Zgodovina</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Orodja strani"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Orodja" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Orodja</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Orodja</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Več možnosti" > <div class="vector-menu-heading"> Dejanja </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Hermann_Weyl"><span>Preberi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&action=history"><span>Zgodovina</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Splošno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:KajSePovezujeSem/Hermann_Weyl" title="Seznam vseh strani, ki se povezujejo sem [j]" accesskey="j"><span>Kaj se povezuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:RecentChangesLinked/Hermann_Weyl" rel="nofollow" title="Zadnje spremembe na straneh, s katerimi se povezuje ta stran [k]" accesskey="k"><span>Povezane spremembe</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:PosebneStrani" title="Seznam vseh posebnih strani [q]" accesskey="q"><span>Posebne strani</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&oldid=6230553" title="Trajna povezava na to redakcijo strani"><span>Trajna povezava</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&action=info" title="Več informacij o tej strani"><span>Podatki o strani</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Navedi&page=Hermann_Weyl&id=6230553&wpFormIdentifier=titleform" title="Informacije o tem, kako navajati to stran"><span>Navedba članka</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:UrlQ%C4%B1sald%C4%B1c%C4%B1s%C4%B1&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FHermann_Weyl"><span>Pridobi skrajšani URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrKodu&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FHermann_Weyl"><span>Prenesi kodo QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tiskanje/izvoz </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Posebno:Book&bookcmd=book_creator&referer=Hermann+Weyl"><span>Ustvari e-knjigo</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Hermann_Weyl&action=show-download-screen"><span>Prenesi kot PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Hermann_Weyl&printable=yes" title="Različica te strani za tisk [p]" accesskey="p"><span>Različica za tisk</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> V drugih projektih </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Hermann_Weyl" hreflang="en"><span>Wikimedijina zbirka</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://sl.wikiquote.org/wiki/Hermann_Weyl" hreflang="sl"><span>Wikinavedek</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q71029" title="Povezava na ustrezni predmet v podatkovni shrambi [g]" accesskey="g"><span>Predmet v Wikipodatkih</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Orodja strani"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Videz"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div 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#a2a9b1;border-spacing:3px;background-color:#f8f9fa;color:black;margin:0.5em 0 0.5em 1em;padding:0.2em;float:right;clear:right;font-size:88%;line-height:1.5em;width:22em}.mw-parser-output .infobox-header,.mw-parser-output .infobox-label,.mw-parser-output .infobox-above,.mw-parser-output .infobox-full-data,.mw-parser-output .infobox-data,.mw-parser-output .infobox-below,.mw-parser-output .infobox-subheader,.mw-parser-output .infobox-image,.mw-parser-output .infobox-navbar,.mw-parser-output .infobox th,.mw-parser-output .infobox td{vertical-align:top}.mw-parser-output .infobox-label,.mw-parser-output .infobox-data,.mw-parser-output .infobox th,.mw-parser-output .infobox td{text-align:left}.mw-parser-output .infobox .infobox-header,.mw-parser-output .infobox .infobox-subheader,.mw-parser-output .infobox .infobox-image,.mw-parser-output .infobox .infobox-full-data,.mw-parser-output .infobox .infobox-below{text-align:center}.mw-parser-output .infobox .infobox-above,.mw-parser-output .infobox .infobox-title,.mw-parser-output .infobox caption{font-size:125%;font-weight:bold;text-align:center}.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}body.skin-minerva .mw-parser-output .infobox-header,body.skin-minerva .mw-parser-output .infobox-subheader,body.skin-minerva .mw-parser-output .infobox-above,body.skin-minerva .mw-parser-output .infobox-title,body.skin-minerva .mw-parser-output .infobox-image,body.skin-minerva .mw-parser-output .infobox-full-data,body.skin-minerva .mw-parser-output .infobox-below{text-align:center}</style><table class="infobox vcard"><tbody><tr><th colspan="2" class="infobox-above fn" style="background:transparent;text-align:center;">Hermann Klaus Hugo Weyl</th></tr><tr><td colspan="2" class="infobox-image"><span class="wikidata-claim" data-wikidata-property-id="P18" data-wikidata-claim-id="q71029$3B7323BC-04DC-47AF-8C37-A7F14B27011B"><span class="wikidata-snak wikidata-main-snak"><span typeof="mw:File"><a href="/wiki/Slika:Hermann_Weyl_ETH-Bib_Portr_00890.jpg" class="mw-file-description" title="Portret"><img alt="Portret" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hermann_Weyl_ETH-Bib_Portr_00890.jpg/220px-Hermann_Weyl_ETH-Bib_Portr_00890.jpg" decoding="async" width="220" height="228" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hermann_Weyl_ETH-Bib_Portr_00890.jpg/330px-Hermann_Weyl_ETH-Bib_Portr_00890.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hermann_Weyl_ETH-Bib_Portr_00890.jpg/440px-Hermann_Weyl_ETH-Bib_Portr_00890.jpg 2x" data-file-width="462" data-file-height="479" /></a></span></span></span></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Rojstvo</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><span class="wikidata-claim" data-wikidata-property-id="P1477" data-wikidata-claim-id="Q71029$cb5457c1-4837-c37f-f382-2ae22ddd1d49"><span class="wikidata-snak wikidata-main-snak"><span class="lang" lang="de">Hermann Klaus Hugo Weyl</span></span></span><br /><span class="wikidata-claim" data-wikidata-property-id="P569" data-wikidata-claim-id="q71029$17287516-9BEC-41F2-9119-39B2EE679D58"><span class="wikidata-snak wikidata-main-snak"><span style="white-space:nowrap;"><a href="/wiki/9._november" title="9. november">9. november</a> <a href="/wiki/1885" title="1885">1885</a></span><span style="display:none">(<span class="bday">{{padleft:1885|4|0}}-{{padleft:11|2|0}}-{{padleft:9|2|0}}</span>)</span></span><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;_1-0" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q35127&quot;_data-entity-id=&quot;Q547473&quot;&gt;MacTutor_History_of_Mathematics_archive&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_1994.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q547473]]&lt;/div&gt;_2-0" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q35127&quot;_data-entity-id=&quot;Q547473&quot;&gt;MacTutor_History_of_Mathematics_archive&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_1994.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q547473]]&lt;/div&gt;-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup><a href="https://www.wikidata.org/wiki/Q71029#P569" class="extiw" title="d:Q71029">[…]</a></sup></span><br /><span class="wikidata-claim" data-wikidata-property-id="P19" data-wikidata-claim-id="q71029$31655F42-E3C4-4C15-9377-62C749C22DE3"><span class="wikidata-snak wikidata-main-snak"><span class="iw" data-title="Elmshorn"><a href="/w/index.php?title=Elmshorn&action=edit&redlink=1" class="new" title="Elmshorn (stran ne obstaja)">Elmshorn</a><sup class="noprint"><a href="https://www.wikidata.org/wiki/Q6845" class="extiw" title="d:Q6845"><span style="font-style:normal; font-weight:normal;" title="Članek «Elmshorn» v Wikipodatkih">[d]</span></a></sup></span></span><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-0" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-1" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></span></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Smrt</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><span class="wikidata-claim" data-wikidata-property-id="P570" data-wikidata-claim-id="q71029$602F67F5-C03D-4F92-8653-65C13A8156F1"><span class="wikidata-snak wikidata-main-snak"><span style="white-space:nowrap;"><a href="/wiki/8._december" title="8. december">8. december</a> <a href="/wiki/1955" title="1955">1955</a></span><span style="display:none">(<span class="dday">{{padleft:1955|4|0}}-{{padleft:12|2|0}}-{{padleft:8|2|0}}</span>)</span></span><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;_1-1" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <span style="white-space:nowrap;">(70 let)</span></span><br /><span class="wikidata-claim" data-wikidata-property-id="P20" data-wikidata-claim-id="Q71029$7480BBAF-01BA-4CF6-82E6-17B2B7F2ED12"><span class="wikidata-snak wikidata-main-snak"><a href="/wiki/Z%C3%BCrich" title="Zürich">Zürich</a></span><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-2" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-3" class="reference"><a href="#cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></span></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Bivališče</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><span typeof="mw:File"><a href="/wiki/Slika:Flag_of_Germany_(1867%E2%80%931918).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Flag_of_Germany_%281867%E2%80%931918%29.svg/22px-Flag_of_Germany_%281867%E2%80%931918%29.svg.png" decoding="async" width="22" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Flag_of_Germany_%281867%E2%80%931918%29.svg/33px-Flag_of_Germany_%281867%E2%80%931918%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Flag_of_Germany_%281867%E2%80%931918%29.svg/44px-Flag_of_Germany_%281867%E2%80%931918%29.svg.png 2x" data-file-width="900" data-file-height="600" /></a></span> <a href="/wiki/Nem%C5%A1ko_cesarstvo" title="Nemško cesarstvo">Nemško cesarstvo</a> <br /> <span typeof="mw:File"><a href="/wiki/Slika:Flag_of_Switzerland.svg" class="mw-file-description" title="Zastava Švice"><img alt="Zastava Švice" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/25px-Flag_of_Switzerland.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/38px-Flag_of_Switzerland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/50px-Flag_of_Switzerland.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/%C5%A0vica" title="Švica">Švica</a> <br /> <span class="mw-image-border" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/20px-Flag_of_the_United_States.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/30px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/40px-Flag_of_the_United_States.svg.png 2x" data-file-width="1235" data-file-height="650" /></span></span> <a href="/wiki/Zdru%C5%BEene_dr%C5%BEave_Amerike" title="Združene države Amerike">ZDA</a></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Narodnost</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><span class="flagicon"><span class="mw-image-border" typeof="mw:File"><a href="/wiki/Nem%C4%8Dija" title="Nemčija"><img alt="Nemčija" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" decoding="async" width="23" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" data-file-width="1000" data-file-height="600" /></a></span></span> <a href="/wiki/Nemci" title="Nemci">nemška</a></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Področja</th><td class="infobox-data category" style="vertical-align:middle;line-height:1.3em;"><a href="/wiki/Matematika" title="Matematika">matematika</a>, <a href="/wiki/Matemati%C4%8Dna_fizika" title="Matematična fizika">matematična fizika</a></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Ustanove</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><a href="/wiki/In%C5%A1titut_za_vi%C5%A1ji_%C5%A1tudij" class="mw-redirect" title="Inštitut za višji študij">Inštitut za višji študij</a> <br /> <a href="/wiki/Univerza_v_G%C3%B6ttingenu" title="Univerza v Göttingenu">Univerza v Göttingenu</a> <br /><a href="/wiki/%C5%A0vicarska_dr%C5%BEavna_tehni%C5%A1ka_visoka_%C5%A1ola_Z%C3%BCrich" title="Švicarska državna tehniška visoka šola Zürich">ETH Zürich</a></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;"><span class="nowrap"><a href="/wiki/Alma_mater" title="Alma mater">Alma mater</a></span></th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><a href="/wiki/Univerza_v_G%C3%B6ttingenu" title="Univerza v Göttingenu">Univerza v Göttingenu</a></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Mentor doktorske<br />disertacije</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Znani študenti</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><a href="/w/index.php?title=Alexander_Weinstein&action=edit&redlink=1" class="new" title="Alexander Weinstein (stran ne obstaja)">Alexander Weinstein</a> <span style="font-size:85%;">(1921)</span> <br /> <a href="/w/index.php?title=Ernst_Max_Mohr&action=edit&redlink=1" class="new" title="Ernst Max Mohr (stran ne obstaja)">Ernst Max Mohr</a> <span style="font-size:85%;">(1933)</span> <br /> <a href="/w/index.php?title=Saunders_Mac_Lane&action=edit&redlink=1" class="new" title="Saunders Mac Lane (stran ne obstaja)">Saunders Mac Lane</a> <span style="font-size:85%;">(1934)</span></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Poznan po</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><style data-mw-deduplicate="TemplateStyles:r5911185">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><a href="/w/index.php?title=Peter-Weylov_izrek&action=edit&redlink=1" class="new" title="Peter-Weylov izrek (stran ne obstaja)">Peter-Weylov izrek</a></li><li><a href="/w/index.php?title=Weylov_kriterij&action=edit&redlink=1" class="new" title="Weylov kriterij (stran ne obstaja)">Weylov kriterij</a></li><li><a href="/w/index.php?title=Weylov_postulat&action=edit&redlink=1" class="new" title="Weylov postulat (stran ne obstaja)">Weylov postulat</a></li><li><a href="/w/index.php?title=Weylov_skalar&action=edit&redlink=1" class="new" title="Weylov skalar (stran ne obstaja)">Weylov skalar</a></li><li><a href="/wiki/Weylov_spinor" class="mw-redirect" title="Weylov spinor">Weylov spinor</a></li><li><a href="/w/index.php?title=Weylov_tenzor&action=edit&redlink=1" class="new" title="Weylov tenzor (stran ne obstaja)">Weylov tenzor</a></li><li><a href="/w/index.php?title=Weylova_algebra&action=edit&redlink=1" class="new" title="Weylova algebra (stran ne obstaja)">Weylova algebra</a></li><li><a href="/w/index.php?title=Weylova_domneva_o_ukrivljenosti&action=edit&redlink=1" class="new" title="Weylova domneva o ukrivljenosti (stran ne obstaja)">Weylova domneva o ukrivljenosti</a></li><li><a href="/wiki/Weylova_ena%C4%8Dba" title="Weylova enačba">Weylova enačba</a></li><li><a href="/w/index.php?title=Weylova_formula_karakterjev&action=edit&redlink=1" class="new" title="Weylova formula karakterjev (stran ne obstaja)">Weylova formula karakterjev</a></li><li><a href="/w/index.php?title=Weylova_grupa&action=edit&redlink=1" class="new" title="Weylova grupa (stran ne obstaja)">Weylova grupa</a></li><li><a href="/w/index.php?title=Weylova_polkovina&action=edit&redlink=1" class="new" title="Weylova polkovina (stran ne obstaja)">Weylova polkovina</a></li><li><a href="/w/index.php?title=Weylova_transformacija&action=edit&redlink=1" class="new" title="Weylova transformacija (stran ne obstaja)">Weylova transformacija</a></li><li><a href="/w/index.php?title=Weylova_vsota&action=edit&redlink=1" class="new" title="Weylova vsota (stran ne obstaja)">Weylova vsota</a></li><li>...</li></ul></div></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Pomembne nagrade</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><a href="/w/index.php?title=Nagrada_Loba%C4%8Devskega&action=edit&redlink=1" class="new" title="Nagrada Lobačevskega (stran ne obstaja)">nagrada Lobačevskega</a> <span style="font-size:85%;">(1927)</span></td></tr><tr><th scope="row" class="infobox-label" style="background:transparent; padding-top:0.225em;line-height:1.1em; padding-right:0.5em;">Podpis</th><td class="infobox-data" style="vertical-align:middle;line-height:1.3em;"><span class="wikidata-claim" data-wikidata-property-id="P109" data-wikidata-claim-id="Q71029$5121CC7E-914D-436B-95E5-B249196A146B"><span class="wikidata-snak wikidata-main-snak"><span typeof="mw:File"><a href="/wiki/Slika:Hermann_Weyl_signature.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hermann_Weyl_signature.svg/150px-Hermann_Weyl_signature.svg.png" decoding="async" width="150" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hermann_Weyl_signature.svg/225px-Hermann_Weyl_signature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hermann_Weyl_signature.svg/300px-Hermann_Weyl_signature.svg.png 2x" data-file-width="240" data-file-height="61" /></a></span></span></span></td></tr></tbody></table> <p><b>Hermann Klaus Hugo Weyl</b>, <a href="/wiki/Nemci" title="Nemci">nemški</a> <a href="/wiki/Matematik" class="mw-redirect" title="Matematik">matematik</a> in <a href="/wiki/Fizik" title="Fizik">fizik</a>, * <a href="/wiki/9._november" title="9. november">9. november</a> <a href="/wiki/1885" title="1885">1885</a>, <a href="/w/index.php?title=Elmshorn&action=edit&redlink=1" class="new" title="Elmshorn (stran ne obstaja)">Elmshorn</a> pri <a href="/wiki/Hamburg" title="Hamburg">Hamburgu</a>, <a href="/w/index.php?title=Prusija_(kraljestvo)&action=edit&redlink=1" class="new" title="Prusija (kraljestvo) (stran ne obstaja)">Prusija</a>, <a href="/wiki/Nem%C5%A1ko_cesarstvo" title="Nemško cesarstvo">Nemško cesarstvo</a> (sedaj <a href="/wiki/Nem%C4%8Dija" title="Nemčija">Nemčija</a>), † <a href="/wiki/8._december" title="8. december">8. december</a> <a href="/wiki/1955" title="1955">1955</a>, <a href="/wiki/Z%C3%BCrich" title="Zürich">Zürich</a>, <a href="/wiki/%C5%A0vica" title="Švica">Švica</a>. </p><p>Čeprav je Weyl večino svojega življenja preživel v Zürichu in nato v <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princetonu</a>, <a href="/wiki/New_Jersey" title="New Jersey">New Jersey</a>, je povezan z matematično tradicijo <a href="/wiki/Univerza_v_G%C3%B6ttingenu" title="Univerza v Göttingenu">Univerze v Göttingenu</a>, ki sta jo predstavljala <a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a> in <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Minkowski</a>. Njegove raziskave so zelo vplivale na <a href="/wiki/Teoreti%C4%8Dna_fizika" title="Teoretična fizika">teoretično fiziko</a>, kot tudi na čista področja, na primer na <a href="/wiki/Teorija_%C5%A1tevil" title="Teorija števil">teorijo števil</a>. Velja za enega najvplivnejših matematikov 20. stoletja in za pomembnega člana <a href="/wiki/In%C5%A1titut_za_vi%C5%A1ji_%C5%A1tudij" class="mw-redirect" title="Inštitut za višji študij">Inštituta za višji študij</a> v času prvih let njegovega obstaja. </p><p>Objavil je strokovna in poljudna dela o <a href="/wiki/Prostor" title="Prostor">prostoru</a>, <a href="/wiki/%C4%8Cas" title="Čas">času</a>, <a href="/wiki/Snov" title="Snov">snovi</a>, <a href="/wiki/Filozofija" title="Filozofija">filozofiji</a>, <a href="/wiki/Logika" title="Logika">logiki</a>, <a href="/wiki/Simetrija" title="Simetrija">simetriji</a> in <a href="/wiki/Zgodovina_matematike" title="Zgodovina matematike">zgodovini matematike</a>. Med prvimi je razumel spoj <a href="/wiki/Splo%C5%A1na_teorija_relativnosti" title="Splošna teorija relativnosti">splošne teorije relativnosti</a> z zakoni <a href="/wiki/Elektrika_in_magnetizem" title="Elektrika in magnetizem">elektromagnetizma</a>. Čeprav noben matematik njegove generacije ni zaobjel <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaréjevega</a> ali Hilbertovega 'univerzalizma', se je Weyl temu zelo približal. <a href="/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah">Atiyah</a> je poudaril, da kadar je pregledoval kakšno matematično snov, je ugotovil, da ga je Weyl prehitel.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Življenje_in_delo"><span id=".C5.BDivljenje_in_delo"></span>Življenje in delo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=1" title="Uredi razdelek: Življenje in delo" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=1" title="Urejanje izvorne kode razdelka: Življenje in delo"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gimnazijo <a href="/w/index.php?title=Christianeum_Hamburg&action=edit&redlink=1" class="new" title="Christianeum Hamburg (stran ne obstaja)">Christianeum</a> je obiskoval v <a href="/wiki/Altona,_Hamburg" title="Altona, Hamburg">Altoni</a> v Hamburgu, kjer je že tam opozoril na svoj matematični dar.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Ravnatelj Hilbert, ga je napotil v <a href="/wiki/G%C3%B6ttingen" title="Göttingen">Göttingen</a> k svojemu bratrancu v uk. Med letoma 1904 in 1908 je študiral matematiko in fiziko v Göttingenu in <a href="/wiki/M%C3%BCnchen" title="München">Münchnu</a>. Leta 1908 je <a href="/wiki/Doktorat" title="Doktorat">doktoriral</a> pod Hilbertovim mentorstvom z dizertacijo <i>Singularne integralske enačbe s posebnim upoštevanjem Fourierovih integralskih izrekov</i> (<i>Singuläre Integralgleichungen mit besonder Berücksichtigung des Fourierschen Integraltheorems</i>).<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Leta 1910 je <a href="/w/index.php?title=Habilitacija&action=edit&redlink=1" class="new" title="Habilitacija (stran ne obstaja)">habilitiral</a> v <a href="/w/index.php?title=Privatni_docent&action=edit&redlink=1" class="new" title="Privatni docent (stran ne obstaja)">privatnega docenta</a> s temo <i>O navadnih diferencialnih enačbah s singularnostmi in pripadajočimi razvoji poljubnih funkcij</i> (<i>Über gewöhnliche Differentialgleicklungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen</i>). Ob Hilbertu in <a href="/wiki/Felix_Christian_Klein" title="Felix Christian Klein">Kleinu</a> je postal eden vodilnih tedanjih matematikov. V Göttingenu je ostal do leta 1913, ko se je preselil v Zürich. Tam je na <a href="/wiki/%C5%A0vicarska_dr%C5%BEavna_tehni%C5%A1ka_visoka_%C5%A1ola_Z%C3%BCrich" title="Švicarska državna tehniška visoka šola Zürich">politehniški visoki šoli</a> (ETH) prevzel katedro za geometrijo. V tem času je na ETH delal <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a> in razdeloval podrobnosti splošne teorije relativnosti. Weyl in Einstein sta postala prijatelja. Einstein je na Weyla trajno vplival, saj se je nadvse navdušil nad <a href="/wiki/Matemati%C4%8Dna_fizika" title="Matematična fizika">matematično fiziko</a> in <a href="/w/index.php?title=Diferencialna_geometrija&action=edit&redlink=1" class="new" title="Diferencialna geometrija (stran ne obstaja)">diferencialno geometrijo</a>. Leta 1918 je objavil svoje vplivno delo <i>Prostor, čas, snov</i> (<i><a rel="nofollow" class="external text" href="http://www.archive.org/details/raumzeitmateriev00weyl">Raum, Zeit, Materie</a></i>) o splošni teoriji relativnosti. V letu 1921 je srečal <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Schrödingerja</a>, ki je tedaj postal redni profesor na Univerzi v Zürichu. Postala sta dobra prijatelja. </p><p>Med letoma 1928 in 1929 je bil Weyl gostujoči profesor na <a href="/wiki/Univerza_Princeton" title="Univerza Princeton">Univerzi Princeton</a>. Najprej je zavrnil povabilo, da bi se vrnil v Göttingen, kjer bi nasledil Kleina. Od leta 1930 je predaval na Univerzi v Göttingenu, kjer je prevzel za Hilbertom, ki je odšel v pokoj, vodstvo matematičnega inštituta. Tukaj je vzdržal do leta 1933. Tega leta je za mnogimi svojimi kolegi in za Einsteinom emigriral v ZDA, še posebej zato, ker je bila njegova žena judinja. V ZDA je do upokojitve leta 1951 deloval na novoustanovljenem Inštitutu za višji študij. Po upokojitvi je bil do smrti častni član Inštituta. Do konca življenja je večino časa preživel z ženo v Zürichu, čeprav se je vsako leto za nekaj mesecev vračal v Princeton. </p><p>Pomembna so njegova dela iz <a href="/wiki/Teorija_grup" title="Teorija grup">teorije grup</a> (posebno glede na uporabo v fiziki), nadalje dela iz teorije števil glede na <a href="/w/index.php?title=Aditivna_teorija_%C5%A1tevil&action=edit&redlink=1" class="new" title="Aditivna teorija števil (stran ne obstaja)">aditivno teorijo števil</a> (<a href="/w/index.php?title=Weylova_vsota&action=edit&redlink=1" class="new" title="Weylova vsota (stran ne obstaja)">Weylova vsota</a>) in še dela iz teorije <a href="/wiki/Diferencialna_ena%C4%8Dba" title="Diferencialna enačba">diferencialnih</a> in <a href="/w/index.php?title=Integralska_ena%C4%8Dba&action=edit&redlink=1" class="new" title="Integralska enačba (stran ne obstaja)">integralskih enačb</a>. Znan je tudi v <a href="/wiki/Fizikalna_kozmologija" class="mw-redirect" title="Fizikalna kozmologija">fizikalni kozmologiji</a> kjer je s <a href="/w/index.php?title=Weylov_postulat&action=edit&redlink=1" class="new" title="Weylov postulat (stran ne obstaja)">svojim postulatom</a> vpeljal vrsto <a href="/wiki/Kozmolo%C5%A1ko_na%C4%8Delo" title="Kozmološko načelo">kozmološkega načela</a>. </p><p>Weyl je pisal s književnim, skoraj pesniškim slogom, ki ni prestal tudi z nujnim prehodom na angleščino. V svojem uvodu v <i>Klasične grupe</i> iz leta 1939 je v svojem običajnem zanosu zapisal, »da so bogovi naložili mojemu pisanju jarem tujega jezika, ki ga ob moji zibelki niso peli,« itd. Po njem »izražanje in oblika pomenita skoraj več kot znanje.« </p><p>Iz prvega zakona s Helene Joseph iz Maklenburga, filozofinjo in prevajalko španske književnosti, je imel Weyl dva sinova, <a href="/w/index.php?title=Fritz_Joachim_Weyl&action=edit&redlink=1" class="new" title="Fritz Joachim Weyl (stran ne obstaja)">Fritza Joachima</a> (1915–1977), ki je tudi sam postal matematik, in Michaela. Po smrti njegove prve žene leta 1948 se je Weyl leta 1950 oženil z Elleno Bär iz Züricha. Najbolj znani Weylovi učenci so: <a href="/w/index.php?title=Alexander_Weinstein&action=edit&redlink=1" class="new" title="Alexander Weinstein (stran ne obstaja)">Weinstein</a>, <a href="/w/index.php?title=Ernst_Max_Mohr&action=edit&redlink=1" class="new" title="Ernst Max Mohr (stran ne obstaja)">Mohr</a>, <a href="/w/index.php?title=Saunders_Mac_Lane&action=edit&redlink=1" class="new" title="Saunders Mac Lane (stran ne obstaja)">Mac Lane</a> in <a href="/w/index.php?title=Gerhard_Gentzen&action=edit&redlink=1" class="new" title="Gerhard Gentzen (stran ne obstaja)">Gentzen</a>. </p><p>Matematika ga je zanimala in mamila na vso moč na široko in vsak košček te pisane širine je obogatil. V teoriji analitičnih funkcij je zgradil sodoben pogled na <a href="/wiki/Riemannova_ploskev" title="Riemannova ploskev">Riemannove ploskve</a>, v teoriji števil je kot močno orodje uporabil <a href="/w/index.php?title=Trigonometri%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Trigonometrična vrsta (stran ne obstaja)">trigonometrične vrste</a>, po svoje se je lotil robnih nalog in integralskih enačb, skupaj z <a href="/wiki/Luitzen_Egbertus_Jan_Brouwer" title="Luitzen Egbertus Jan Brouwer">Broewerjem</a> je zaoral novo brazdo v osnove matematike, <a href="/w/index.php?title=Intuicionizem&action=edit&redlink=1" class="new" title="Intuicionizem (stran ne obstaja)">intuicionizem</a>, ki priznava izključno samo konstruktivne <a href="/wiki/Matemati%C4%8Dni_dokaz" title="Matematični dokaz">dokazovalne</a> postopke. Ukvarjal se je s problemi <a href="/wiki/Samopodobnost" title="Samopodobnost">samopodobnosti</a> <a href="/wiki/Fraktal" title="Fraktal">fraktalnih</a> <a href="/wiki/Mno%C5%BEica" title="Množica">množic</a>. Leta 1917, eno leto po nastanku je že predaval o <a href="/wiki/Splo%C5%A1na_teorija_relativnosti" title="Splošna teorija relativnosti">splošni teoriji relativosti</a>. </p><p>Weyl je zelo dobro poznal in cenil <a href="/wiki/Josip_Plemelj" title="Josip Plemelj">Plemlja</a>. 21. januarja 1952 mu je v pismu med drugim zapisal: »Zelo sem vesel, da sem po dolgih letih spet slišal o Vas. Od tedaj, od naše skupne matematične mladosti, ko ste objavili čudovito razpravo o Riemannovem problemu o monodromiji in nagrajeni spis o potencialni teoriji, sem Vaš veliki občudovalec. Upam, da ste v dobrem zdravju.«<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Geometrijski_temelji_mnogoterosti_in_fizike">Geometrijski temelji mnogoterosti in fizike</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=2" title="Uredi razdelek: Geometrijski temelji mnogoterosti in fizike" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=2" title="Urejanje izvorne kode razdelka: Geometrijski temelji mnogoterosti in fizike"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>V letu 1913 je Weyl objavil delo <i>Predstava Riemannove ploskve</i> (<i>Die Idee der Riemannschen Fläche</i>), v katerem je podal poenoteno obravnavo <a href="/wiki/Riemannova_ploskev" title="Riemannova ploskev">Riemannovih ploskev</a>, ki je nastala med njegovimi predavanji v jesenskem semestru 1911/12. Tu je uporabil <a href="/wiki/Topologija" title="Topologija">topologijo</a> množic <a href="/wiki/To%C4%8Dka_(geometrija)" title="Točka (geometrija)">točk</a>, da bi bila teorija Riemannovih ploskev strožja. Ta način je kasneje uporabil pri delu o <a href="/wiki/Mnogoterost" title="Mnogoterost">mnogoterostih</a>. V ta namen je prevzel Brouwerjevo zgodnejše delo v topologiji in prvi uporabil <a href="/w/index.php?title=Splo%C5%A1na_topologija&action=edit&redlink=1" class="new" title="Splošna topologija (stran ne obstaja)">splošno topologijo</a>, da bi tedanjo teorijo Riemannovih ploskev algebrskih funkcij postavil na trdnejše, točne temelje, ki bi zadovoljili Hilbertove zahteve po vsebinski in metodološki strogosti. </p><p>Leta 1918 je izšla njegova knjiga o prostoru, času in snovi <i>Prostor, čas, snov</i> (<i>Raum, Zeit, Materie</i>), uspešnica, ki je do leta 1923 doživela kar pet nemških izdaj pa še angleški in francoski (zadnjemu se je Weyl odpovedal, tako svoboden je bil). Za uvod v splošno teorijo relativnosti je na novo osmislil Riemannovo diferencialno geometrijo, zanjo pa je potreboval trdne <a href="/wiki/Algebra" title="Algebra">algebrske</a> in topološke pojme o našem <a href="/wiki/Evklidski_prostor" title="Evklidski prostor">evklidskem prostoru</a>. Zato velja prvo poglavje knjige <i>Prostor, čas, snov</i> za zibelko evklidskega prostora. V uvodu je razglabljal o <a href="/wiki/%C4%8Cas" title="Čas">času</a> in <a href="/wiki/Prostor" title="Prostor">prostoru</a> kot o eksistenčnih oblikah realnega sveta, o <a href="/wiki/Snov" title="Snov">snovi</a> kot njegovi substanci. Večno tekoči čas, skrivnost naše časovne zavesti, je po njegovem osrednje <a href="/wiki/Metafizika" title="Metafizika">metafizično</a> vprašanje, ki ga poskuša pojasniti in rešiti <a href="/wiki/Filozofija" title="Filozofija">filozofija</a>, odkar je. Prostor, pravi, pa je že pred starimi Grki postal predmet znanstvene obravnave, ki jo odlikujeta največja jasnost in zanesljivost. Z Einsteinom, je sodil, so se trdni temelji <a href="/wiki/Naravoslovje" title="Naravoslovje">naravoslovja</a> zamajali, vendar le zato, da napravijo prostor za svobodnejši in globlji pogled na stvari. Od tod ni poti nazaj, razvoj <a href="/wiki/Znanost" title="Znanost">znanosti</a> lahko preseže današnje poglede, toda k stari ozki in togi shemi se ne more vrniti več. Iz preprostega zdaj mu zraste čas kot <a href="/wiki/Razse%C5%BEnost" class="mw-redirect" title="Razsežnost">enorazsežni</a> kontinuum, iz prav takšnega tukaj pa se povzpne do pojma prostora. Prostor se doživlja v <a href="/wiki/Gibanje" title="Gibanje">gibanju</a>, v gibljivosti <a href="/wiki/Telo_(fizika)" title="Telo (fizika)">teles</a> v njem. Že <a href="/wiki/Hermann_Ludwig_Ferdinand_von_Helmholtz" title="Hermann Ludwig Ferdinand von Helmholtz">Helmholtz</a> je iskal osnove geometrije v tistih značilnostih prostora, ki jih odražajo gibanja <a href="/wiki/Togo_telo" title="Togo telo">togih teles</a>. Isto togo telo je enkrat tukaj, drugič tam. Ali: togo telo je tukaj, tam pa je temu telesu kongruentno telo. Za kongruentnostjo pa tiči <a href="/wiki/Grupa_(matematika)" class="mw-redirect" title="Grupa (matematika)">grupa</a>, grupa togih premikov prostora. Potem so mu bili pomembni posebni, vzporedni premiki (translacije). Kako je znotraj grupe vseh premikov moč razpoznati translacije? Napisal je: »Imejmo premik (gibanje) <i>T</i>. Brž ko za vsak par točk <i>A</i>, <i>B</i> najdemo premik, ki preslika <i>A</i> v <i>B</i> in komutira s <i>T</i>, je <i>T</i> translacija. Množica vseh translacij sestavlja komutativno grupo. Zapišimo jo aditivno, superpozicijo označimo z znakom + in jo imenujmo vsoto. Translacija je natanko določena s sliko ene točke. Točka <i>A</i> in njena slika <i>A´</i> sestavljata urejen par <i>AA´</i>. Urejen par točk povežemo z usmerjeno daljico, ki kaže od <i>A</i> proti <i>A´</i>. Isti translaciji ustreza cela družina daljic <i>AA´</i>, vsaka točka prostora je lahko začetna točka take daljice. Računanje s translacijami spremlja računanje z usmerjenimi daljicami. V translacijah in v usmerjenih daljicah (raje: v ekvivalentnih razredih usmerjenih daljic) lahko vidimo različni popredmetenji iste abstraktne strukture, aditivne grupe vektorjev.« V aditivno grupo vektorjev je uvedel novo operacijo, produkt s številom. Najprej produkt s celim številom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ma={\vec {\mathbf {a} }}+{\vec {\mathbf {a} }}+...+{\vec {\mathbf {a} }}\!\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ma={\vec {\mathbf {a} }}+{\vec {\mathbf {a} }}+...+{\vec {\mathbf {a} }}\!\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/241ca23f076f61fff22cfbee36dd8673c730a5d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.826ex; height:2.509ex;" alt="{\displaystyle ma={\vec {\mathbf {a} }}+{\vec {\mathbf {a} }}+...+{\vec {\mathbf {a} }}\!\,}"></span></dd></dl> <p>z <i>m</i> členi, če je <i>m</i> > 0, za negativen <i>m</i> naj bo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m{\vec {\mathbf {a} }}=-(-m){\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−<!-- − --></mo> <mo stretchy="false">(</mo> <mo>−<!-- − --></mo> <mi>m</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m{\vec {\mathbf {a} }}=-(-m){\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf809165a543076ae21150576c0ad87e4ebafcad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.204ex; height:2.843ex;" alt="{\displaystyle m{\vec {\mathbf {a} }}=-(-m){\vec {\mathbf {a} }}}"></span>, za <i>m</i> = 0 pa seveda <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0{\vec {\mathbf {a} }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0{\vec {\mathbf {a} }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a414afd3e6ed888fc51363940cc910d64d7f1dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.723ex; height:2.343ex;" alt="{\displaystyle 0{\vec {\mathbf {a} }}=0}"></span>. Produkt vektorja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span> z <a href="/wiki/Recipro%C4%8Dna_vrednost" title="Recipročna vrednost">recipročno vrednostjo</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e50c6400a820fbab85cf584ccd835e75ad32210b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.373ex; height:2.676ex;" alt="{\displaystyle m^{-1}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\in \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\in \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42411e85d874a733209223302bbd8d5e3ad04cb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.559ex; height:2.176ex;" alt="{\displaystyle m\in \mathbb {N} }"></span> naj bo vektor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m^{-1}{\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m^{-1}{\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e697c55fdb0407d07c861932050ddc97fd06b90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.673ex; height:2.676ex;" alt="{\displaystyle m^{-1}{\vec {\mathbf {a} }}}"></span>, da se bo <i>m</i> členov, enakih <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m^{-1}{\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m^{-1}{\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e697c55fdb0407d07c861932050ddc97fd06b90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.673ex; height:2.676ex;" alt="{\displaystyle m^{-1}{\vec {\mathbf {a} }}}"></span>, seštelo v vsoto <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m^{-1}{\vec {\mathbf {a} }}+m^{-1}{\vec {\mathbf {a} }}+...+m^{-1}{\vec {\mathbf {a} }}={\vec {\mathbf {a} }}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m^{-1}{\vec {\mathbf {a} }}+m^{-1}{\vec {\mathbf {a} }}+...+m^{-1}{\vec {\mathbf {a} }}={\vec {\mathbf {a} }}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd8254b683b23c334f08607ed7f92eb2897f9584" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:31.621ex; height:2.843ex;" alt="{\displaystyle m^{-1}{\vec {\mathbf {a} }}+m^{-1}{\vec {\mathbf {a} }}+...+m^{-1}{\vec {\mathbf {a} }}={\vec {\mathbf {a} }}\!\,.}"></span></dd></dl> <p>Geometrijsko pomeni to, da se da vsaka translacija sestaviti iz <i>m</i> enakih manjših translacij, vsaka daljica razdeliti na <i>m</i> delov. Naslednji korak do produkta z <a href="/wiki/Racionalno_%C5%A1tevilo" title="Racionalno število">racionalnim številom</a> <i>m</i>/<i>n</i> je jasen. Nazadnje se z zahtevo po zveznosti omogoči še množenje s poljubnim realnim številom. Za geometrijo je torej aditivna translacijska grupa premalo, zveznost terja, naj translacije sestavljajo realni <a href="/wiki/Vektorski_prostor" title="Vektorski prostor">vektorski prostor</a>. Zato je pač Weyl najprej definiral realni vektorski prostor. To je znana, že večkrat ponovljena definicija, nazadnje se jo sreča pri <a href="/wiki/Giuseppe_Peano" title="Giuseppe Peano">Peanu</a>. V Weylovih časih je bil ta del Peanove ustvarjalnosti pozabljen. Za <a href="/wiki/Evklidska_geometrija" title="Evklidska geometrija">evklidsko geometrijo</a> je abstraktna in aksiomatska osnova evklidski vektorski prostor, ki ga je Weyl prvi opredelil. V evklidskem prostoru je ob vsoti vektorjev in ob produktu vektorja s skalarjem definirana tretja operacija, <a href="/wiki/Skalarni_produkt" title="Skalarni produkt">skalarni produkt</a>. Skalarni produkt priredi vektorjema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span> in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {b} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {b} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a46415c564b5c2745811a7748334a63791994c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.843ex;" alt="{\displaystyle {\vec {\mathbf {b} }}}"></span> število, ki se ga označi z <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94ca3839611afb273344b393c79850b6635daee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.628ex; height:3.343ex;" alt="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})}"></span>. Osnovni aksiomi zanj pravijo: Je <a href="/wiki/Komutativnost" title="Komutativnost">komutativnen</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {b} }},{\vec {\mathbf {a} }})=({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\!\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {b} }},{\vec {\mathbf {a} }})=({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\!\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96400935512024892b3ad4f4c6334573208ac200" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.001ex; height:3.343ex;" alt="{\displaystyle ({\vec {\mathbf {b} }},{\vec {\mathbf {a} }})=({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\!\,,}"></span></dd></dl> <p>je <a href="/w/index.php?title=Bilinearnost&action=edit&redlink=1" class="new" title="Bilinearnost (stran ne obstaja)">bilinearen</a> in zaradi komutativnosti je dovolj, če je v prvem faktorju: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }}_{1}+{\vec {\mathbf {a} }}_{2},{\vec {\mathbf {b} }})=({\vec {\mathbf {a} }}_{1},{\vec {\mathbf {b} }})+({\vec {\mathbf {a} }}_{2},{\vec {\mathbf {b} }})(\lambda {\vec {\mathbf {a} }},{\vec {\mathbf {b} }})=\lambda ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>λ<!-- λ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>λ<!-- λ --></mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }}_{1}+{\vec {\mathbf {a} }}_{2},{\vec {\mathbf {b} }})=({\vec {\mathbf {a} }}_{1},{\vec {\mathbf {b} }})+({\vec {\mathbf {a} }}_{2},{\vec {\mathbf {b} }})(\lambda {\vec {\mathbf {a} }},{\vec {\mathbf {b} }})=\lambda ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dcd00ead52f9739a0fff5502319623c153c5998" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:48.892ex; height:3.343ex;" alt="{\displaystyle ({\vec {\mathbf {a} }}_{1}+{\vec {\mathbf {a} }}_{2},{\vec {\mathbf {b} }})=({\vec {\mathbf {a} }}_{1},{\vec {\mathbf {b} }})+({\vec {\mathbf {a} }}_{2},{\vec {\mathbf {b} }})(\lambda {\vec {\mathbf {a} }},{\vec {\mathbf {b} }})=\lambda ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\!\,.}"></span></dd></dl> <p>Je pozitivno <a href="/w/index.php?title=Definitnost&action=edit&redlink=1" class="new" title="Definitnost (stran ne obstaja)">definiten</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})\geq 0\qquad ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})=0\iff {\vec {\mathbf {a} }}=0\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>≥<!-- ≥ --></mo> <mn>0</mn> <mspace width="2em" /> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⟺<!-- ⟺ --></mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})\geq 0\qquad ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})=0\iff {\vec {\mathbf {a} }}=0\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fea8690ef2687c2e0cad8f605e56b0e6c1465755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.156ex; height:2.843ex;" alt="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})\geq 0\qquad ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})=0\iff {\vec {\mathbf {a} }}=0\!\,.}"></span></dd></dl> <p>V evklidskem prostoru se lahko merijo dolžine. Ker je skalarni produkt pozitvno definiten, se lahko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2959c71377fbd66067d68be5b78dac89ab2a27e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.442ex; height:2.843ex;" alt="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})}"></span> koreni in kvadratni koren proglasi za normo vektorja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\vec {\mathbf {a} }}|={\sqrt {({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})}}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </msqrt> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\vec {\mathbf {a} }}|={\sqrt {({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})}}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac684fa6b3bad621bb8b434d91df14d08af80924" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.104ex; height:4.843ex;" alt="{\displaystyle |{\vec {\mathbf {a} }}|={\sqrt {({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})}}\!\,.}"></span></dd></dl> <p>Naj se vzameta dva vektorja, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>≠<!-- ≠ --></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70bc30ae122d94c8229af398618e3835cf045ba0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.56ex; height:2.843ex;" alt="{\displaystyle {\vec {\mathbf {a} }}\neq 0}"></span> in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {b} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {b} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a46415c564b5c2745811a7748334a63791994c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.843ex;" alt="{\displaystyle {\vec {\mathbf {b} }}}"></span>. Pri vsakem <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ<!-- λ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\lambda {\vec {\mathbf {a} }}+{\vec {\mathbf {b} }},\lambda {\vec {\mathbf {a} }}+{\vec {\mathbf {b} }})\geq 0\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>λ<!-- λ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>λ<!-- λ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>≥<!-- ≥ --></mo> <mn>0</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\lambda {\vec {\mathbf {a} }}+{\vec {\mathbf {b} }},\lambda {\vec {\mathbf {a} }}+{\vec {\mathbf {b} }})\geq 0\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5f9d2d299c3550c15c401baabdd104ee6daf2a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.712ex; height:3.343ex;" alt="{\displaystyle (\lambda {\vec {\mathbf {a} }}+{\vec {\mathbf {b} }},\lambda {\vec {\mathbf {a} }}+{\vec {\mathbf {b} }})\geq 0\!\,.}"></span></dd></dl> <p>Upošteva se, da je skalarni produkt bilinearen in komutativen, pa se lahko levo stran napiše kot kvadratni polinom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})\lambda \lambda +2({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\lambda +({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\geq 0\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mi>λ<!-- λ --></mi> <mi>λ<!-- λ --></mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mi>λ<!-- λ --></mi> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>≥<!-- ≥ --></mo> <mn>0</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})\lambda \lambda +2({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\lambda +({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\geq 0\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cb625b7f8569c8484b0983dc7ecbf9dd3570ae7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.701ex; height:3.343ex;" alt="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})\lambda \lambda +2({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\lambda +({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\geq 0\!\,.}"></span></dd></dl> <p>Negativna kvadratna funkcija pa ima nepozitivno diskriminanto, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\lambda -({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mi>λ<!-- λ --></mi> <mo>−<!-- − --></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>≤<!-- ≤ --></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\lambda -({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2abcf4d5b1756ccafea159196f19597e9823afab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.341ex; height:3.343ex;" alt="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})\lambda -({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\leq 0}"></span>. Od tod Cauchyjeva ocena: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})|\leq |{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≤<!-- ≤ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})|\leq |{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e56655a5647e4bc691db3748d53cc39f9d7cffb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.039ex; height:3.343ex;" alt="{\displaystyle |({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})|\leq |{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|\!\,.}"></span></dd></dl> <p>Iz Cauchyjeve ocene izhaja tudi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }}|\lambda =({\vec {\mathbf {a} }}+{\vec {\mathbf {b} }},{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }})=({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})+2({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})+({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\leq |{\vec {\mathbf {a} }}|\lambda +2|{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|+|{\vec {\mathbf {b} }}|\lambda \!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>λ<!-- λ --></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>≤<!-- ≤ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>λ<!-- λ --></mi> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>λ<!-- λ --></mi> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }}|\lambda =({\vec {\mathbf {a} }}+{\vec {\mathbf {b} }},{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }})=({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})+2({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})+({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\leq |{\vec {\mathbf {a} }}|\lambda +2|{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|+|{\vec {\mathbf {b} }}|\lambda \!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9af7d509df1de82983cd56e468f589101e75ec62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:76.335ex; height:3.343ex;" alt="{\displaystyle |{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }}|\lambda =({\vec {\mathbf {a} }}+{\vec {\mathbf {b} }},{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }})=({\vec {\mathbf {a} }},{\vec {\mathbf {a} }})+2({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})+({\vec {\mathbf {b} }},{\vec {\mathbf {b} }})\leq |{\vec {\mathbf {a} }}|\lambda +2|{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|+|{\vec {\mathbf {b} }}|\lambda \!\,.}"></span></dd></dl> <p>Nazadnje: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }}|\leq |{\vec {\mathbf {a} }}|+|{\vec {\mathbf {b} }}|\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≤<!-- ≤ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }}|\leq |{\vec {\mathbf {a} }}|+|{\vec {\mathbf {b} }}|\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bda8070a8e41446cb7317bc3f482215563caf97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.877ex; height:3.343ex;" alt="{\displaystyle |{\vec {\mathbf {a} }}+{\vec {\mathbf {b} }}|\leq |{\vec {\mathbf {a} }}|+|{\vec {\mathbf {b} }}|\!\,.}"></span></dd></dl> <p>Kot <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ<!-- ϕ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> med vektorjema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span> in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {b} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {b} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a46415c564b5c2745811a7748334a63791994c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.843ex;" alt="{\displaystyle {\vec {\mathbf {b} }}}"></span> definiramo s: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \phi ={({\vec {\mathbf {a} }},{\vec {\mathbf {b} }}) \over |{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>ϕ<!-- ϕ --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \phi ={({\vec {\mathbf {a} }},{\vec {\mathbf {b} }}) \over |{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95c414aeceeaa31a48878cc98bbd754e38450c21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:15.093ex; height:7.509ex;" alt="{\displaystyle \cos \phi ={({\vec {\mathbf {a} }},{\vec {\mathbf {b} }}) \over |{\vec {\mathbf {a} }}||{\vec {\mathbf {b} }}|}\!\,.}"></span></dd></dl> <p>Zaradi Cauchyjeve ocene je definicija smiselna, desna stran leži med -1 in 1, kot velja za kosinus. V posebnem primeru, ko je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi =\pi /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ<!-- ϕ --></mi> <mo>=</mo> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi =\pi /2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cadf18d50a7f0439bfbcd3256b040e494d80ab6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.141ex; height:2.843ex;" alt="{\displaystyle \phi =\pi /2}"></span> in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \phi =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>ϕ<!-- ϕ --></mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \phi =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/385db81c184dbcc6fbdbac52023456a702c6d279" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.145ex; height:2.509ex;" alt="{\displaystyle \cos \phi =0}"></span>, sta vektorja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span> in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {b} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {b} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a46415c564b5c2745811a7748334a63791994c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.843ex;" alt="{\displaystyle {\vec {\mathbf {b} }}}"></span> pravokotna. Lahko se reče: Vektorja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {a} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {a} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3155912a710b9fd22f385aa6ccc0d4831e506b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:2.343ex;" alt="{\displaystyle {\vec {\mathbf {a} }}}"></span> in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {\mathbf {b} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\mathbf {b} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23a46415c564b5c2745811a7748334a63791994c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.843ex;" alt="{\displaystyle {\vec {\mathbf {b} }}}"></span> sta pravokotna, če je njun skalarni produkt enak 0: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})=0\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})=0\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28874816e5e0595d6e1105981a13803450d29c6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.536ex; height:3.343ex;" alt="{\displaystyle ({\vec {\mathbf {a} }},{\vec {\mathbf {b} }})=0\!\,.}"></span></dd></dl> <p>Weyl je imel pred očmi le končnorazsežne prostore. Pa že ob teh velja poudariti njegovo zaslugo, da je pripeljal skalarni produkt v aksiomatiko. V svojem govoru o Felixu Kleinu (1929) je dejal: »Na vse je gledal brez predsodkov in kolikor je mogel, je poskusil matematiko zbližati z njeno naravoslovno in tehnično uporabo. Upoštevati pa moramo, da igra matematika še drugo, zelo pomembno vlogo pri oblikovanju našega duhovnega lika. Ukvarjanje z matematiko je – tako kot mitologija, književnost ali glasba – ena tistih oblik človekove dejavnosti, ki so zanj najbolj značilne, v njih se izraža človekovo bistvo, težnja k intelektualni sferi življenja, ki je ena od oblik svetovne harmonije. Klein je tožil, »da se v nemški družbi, kot kaže, še ni izoblikovala enotna kultura, ki bi eksaktne znanosti vključevala kot obvezni sestavni del.« Nekakšen prelom, ki ga je zaznati v tej smeri, si najbrž lahko razložimo s povečanim zanimanjem za tehniko, ki tudi široke množice vključuje v kulturo ekzaktnih znanj, čeprav moje osebne izkušnje iz stikov z mladim pokoljenjem tega ne potrjujejo vselej, večkrat sem opazoval, da so mladi ljudje, navdušeni za avtomobilski šport, dostikrat sovražno razpoloženi do teorije in se nikakor niso pripravljeni resno poglobiti v mehaniko.« Pri Weylu sta se na aksiomatski ravni srečali algebrska in metrična zgradba, stari znanki iz konkretnih zgledov. <a href="/wiki/Metrika" title="Metrika">Metrika</a> je prišla v vektorski prostor po ovinku, s skalarnim produktom, vektorski prostor je bil končnorazsežen. Analiza pa je bila pripravljena na več, na združitev zelo splošne metrike in neskončnorazsežnega prostora. Ta spoj je zaživel v delih več avtorjev v tridesetih letih, v delih <a href="/wiki/Stefan_Banach" title="Stefan Banach">Banacha</a>, <a href="/wiki/Norbert_Wiener" title="Norbert Wiener">Wienerja</a> in drugih. </p><p>Skupaj s <a href="/w/index.php?title=Fritz_Peter&action=edit&redlink=1" class="new" title="Fritz Peter (stran ne obstaja)">Petrom</a> je leta 1927 v članku <i>Die Vollstaendigkeit der primitiven Darstellungen einer geschlossenene kontinuirlichen Gruppe</i> prvi obravnaval upodobitve kompaktne grupe. Objavila sta ga v <i><a href="/w/index.php?title=Mathematische_Annalen&action=edit&redlink=1" class="new" title="Mathematische Annalen (stran ne obstaja)">Mathematische Annalen</a></i>. že kot naslov pove, sta sprva obravnavala le kompaktne Liejeve grupe. Invariantni integral nad kompaktno Liejevo grupo je poznal že <a href="/wiki/Adolf_Hurwitz" title="Adolf Hurwitz">Hurwitz</a> in je bil pri roki. Kmalu potem je <a href="/w/index.php?title=Alfr%C3%A9d_Haar&action=edit&redlink=1" class="new" title="Alfréd Haar (stran ne obstaja)">Haar</a> našel invariantni integral nad krajevno kompaktno topološko grupo. Nad kompaktno grupo odlikujejo Haarov integral vse značilnosti, ki sta jih Peter in Weyl uporabila v svoji teoriji. Zato je Peter-Weylova teorija obveljala za vse kompaktne grupe. Osnovni pripomoček je bil integralski operator s simetričnim jedrom. Najprej sta sestavila zvezno simetrično funkcijo nad <i>G</i>, tako pač, da je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h(a^{-1})=h(a)\!\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(a^{-1})=h(a)\!\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11098c9b3f80991ae565f795749ae424f276e61b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.834ex; height:3.176ex;" alt="{\displaystyle h(a^{-1})=h(a)\!\,,}"></span></dd></dl> <p>njej pa priredila operator z jedrom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(a,b)=h(ab^{-1})\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>a</mi> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(a,b)=h(ab^{-1})\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54bf7a86266f650ab1fb2ff030ada8e9e6b4e259" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.588ex; height:3.176ex;" alt="{\displaystyle H(a,b)=h(ab^{-1})\!\,.}"></span></dd></dl> <p>Jedro operatorja je zvezno in simetrično, zato gre po Hilbert-Schmidtovi poti. Na koncu poti sta dognala: kompaktna grupa ima kvečjemu števno mnogo nerazcepnih upodobitev, vse so končnorazsežne. Naj se zapišijo unitarne matrike teh upodobitev, pa se najde števno mnogo funkcij na grupi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{ik}^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>τ<!-- τ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{ik}^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/350f4f8cb9ac3431ee1bcfee66b22e469fc38d09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.672ex; height:3.176ex;" alt="{\displaystyle \tau _{ik}^{k}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k\in \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k\in \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a5bc4b7383031ba693b7433198ead7170954c1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.73ex; height:2.176ex;" alt="{\displaystyle k\in \mathbb {N} }"></span>. Matrični elementi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau _{ik}^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>τ<!-- τ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau _{ik}^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/350f4f8cb9ac3431ee1bcfee66b22e469fc38d09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.672ex; height:3.176ex;" alt="{\displaystyle \tau _{ik}^{k}}"></span> sestavljajo polno ortogonalno bazo v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{(}G)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> </msub> <mi>G</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{(}G)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78464787105e6c0e45aac04c8fe0b99d4fc38381" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.186ex; height:3.176ex;" alt="{\displaystyle L_{(}G)}"></span>. Funkciji <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle fL_{(}G)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> </msub> <mi>G</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle fL_{(}G)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f5a1897cf0f542570c359e70824f299d103094a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.465ex; height:3.176ex;" alt="{\displaystyle fL_{(}G)}"></span> se priredi Fourierovo transformiranko, ki jo sestavlja zaporedje operatorjev: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {f}}_{k}={\overline {f}}(b)T_{b}^{k}db\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msubsup> <mi>d</mi> <mi>b</mi> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {f}}_{k}={\overline {f}}(b)T_{b}^{k}db\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a7d95f0cbe99fec7c59e58179b700c4585ed437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.631ex; height:3.676ex;" alt="{\displaystyle {\overline {f}}_{k}={\overline {f}}(b)T_{b}^{k}db\!\,.}"></span></dd></dl> <p><a href="/wiki/Fourierova_transformacija" title="Fourierova transformacija">Fourierovo transformacijo</a> se obrne s <a href="/wiki/Fourierova_vrsta" title="Fourierova vrsta">Fourierovo vrsto</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {f}}(a)=d_{1}s_{1}{\overline {f}}_{1}(T_{a}^{1})^{-1}+d_{2}s_{1}{\overline {f}}_{2}(T_{a}^{2})^{-1}+d_{3}s_{1}{\overline {f}}_{3}(T_{a}^{3})^{-1}+...\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {f}}(a)=d_{1}s_{1}{\overline {f}}_{1}(T_{a}^{1})^{-1}+d_{2}s_{1}{\overline {f}}_{2}(T_{a}^{2})^{-1}+d_{3}s_{1}{\overline {f}}_{3}(T_{a}^{3})^{-1}+...\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c7b603ca00bd1d3dc8a104a4a6030e30c40abfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:60.447ex; height:3.509ex;" alt="{\displaystyle {\overline {f}}(a)=d_{1}s_{1}{\overline {f}}_{1}(T_{a}^{1})^{-1}+d_{2}s_{1}{\overline {f}}_{2}(T_{a}^{2})^{-1}+d_{3}s_{1}{\overline {f}}_{3}(T_{a}^{3})^{-1}+...\!\,.}"></span></dd></dl> <p>Faktor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b78f5b2abc48e63b987b6d7527caa5aa9b1bb512" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.298ex; height:2.509ex;" alt="{\displaystyle d_{k}}"></span> je spet razsežnost upodobitve <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{a}^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{a}^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72c84a5aa7eb6428403b99d37e80442542f8a78f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.809ex; height:2.843ex;" alt="{\displaystyle T_{a}^{k}}"></span>, pove, da nastopa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{a}^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{a}^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72c84a5aa7eb6428403b99d37e80442542f8a78f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.809ex; height:2.843ex;" alt="{\displaystyle T_{a}^{k}}"></span> v regularni upodobitvi natanko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b78f5b2abc48e63b987b6d7527caa5aa9b1bb512" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.298ex; height:2.509ex;" alt="{\displaystyle d_{k}}"></span>- krat. Brž, ko je grupa končna, ostane od vrste le končna vsota. Nerazcepne upodobitve (v kompleksnem) grupe SO(2) pa so enorazsežne, zato so vsi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b78f5b2abc48e63b987b6d7527caa5aa9b1bb512" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.298ex; height:2.509ex;" alt="{\displaystyle d_{k}}"></span> enaki 1. <a href="/w/index.php?title=Peter-Weylov_izrek&action=edit&redlink=1" class="new" title="Peter-Weylov izrek (stran ne obstaja)">Peter-Weylov izrek</a> je eksistenčni izrek v Hilbertovem duhu, pove, da nerazcepne upodobitve kompaktne grupe obstajajo, da jih je kvečjemu števno mnogo in da so končnorazsežne, kako jih zares izračunati, pa zataji. Dopolnil je <a href="/w/index.php?title=%C3%89lie_Joseph_Cartan&action=edit&redlink=1" class="new" title="Élie Joseph Cartan (stran ne obstaja)">Cartanovo</a> končnorazsežno upodabljanje polenostavnih algebr. </p> <div class="mw-heading mw-heading3"><h3 id="Temelji_matematike"><a href="/wiki/Temelji_matematike" title="Temelji matematike">Temelji matematike</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=3" title="Uredi razdelek: Temelji matematike" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=3" title="Urejanje izvorne kode razdelka: Temelji matematike"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>V delu <i>Kontinuum</i> iz leta 1918 je Weyl razvil logiko <a href="/w/index.php?title=Impredikativnost&action=edit&redlink=1" class="new" title="Impredikativnost (stran ne obstaja)">predikativne analize</a> s pomočjo nižjih nivojev <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russllove</a> <a href="/w/index.php?title=Principia_Mathematica&action=edit&redlink=1" class="new" title="Principia Mathematica (stran ne obstaja)">razvejane teorije tipov</a>. Večino klasičnega <a href="/wiki/Matemati%C4%8Dna_analiza" title="Matematična analiza">računa</a> je lahko razvil brez <a href="/w/index.php?title=Aksim_izbire&action=edit&redlink=1" class="new" title="Aksim izbire (stran ne obstaja)">aksioma izbire</a> ali <a href="/wiki/Dokaz_s_protislovjem" title="Dokaz s protislovjem">dokaza s protislovjem</a> in se ognil <a href="/wiki/Georg_Ferdinand_Cantor" title="Georg Ferdinand Cantor">Cantorjevim</a> <a href="/w/index.php?title=Neskon%C4%8Dna_mno%C5%BEica&action=edit&redlink=1" class="new" title="Neskončna množica (stran ne obstaja)">neskončnim množicam</a>. V tem obdobju se je Weyl prizival na radikalni konstruktivizem nemškega romantičnega, subjektivnega idealista <a href="/wiki/Johann_Gottlieb_Fichte" title="Johann Gottlieb Fichte">Fichteja</a>. </p><p>Kmalu po objavi <i>Kontinuuma</i> se je Weyl popolnoma obrnil k Brouwerjevemu intuicionizmu. V <i>Kontinuumu</i> konstruktabilne točke obstajajo kot diskretne entitete. Želel je <a href="/wiki/Kontinuum_(teorija_mno%C5%BEic)" title="Kontinuum (teorija množic)">kontinuum</a>, ki ne bi bil le skupek točk. Napisal je polemičen članek, v katerem je zase in za Brouwerja napisal: »Midva sva revolucija«. Članek je bil veliko bolj vpliven pri širjenju intuicionizma kot pa izvirna Brouwerjeva dela sama. </p><p><a href="/wiki/George_P%C3%B3lya" title="George Pólya">Pólya</a> in Weyl sta med srečanjem matematikov v Zürichu (9. februarja 1918) stavila o prihodnji usmeritvi matematike. Weyl je napovedal, da bodo naslednjih 20 let matematiki spoznali popolno nedoločenost pojmov, kot so: <a href="/wiki/Realno_%C5%A1tevilo" title="Realno število">realna števila</a>, množice in <a href="/wiki/%C5%A0tevna_mno%C5%BEica" title="Števna množica">števnost</a>, ter naprej, da je vprašanje o pravilnosti ali nepravilnosti <a href="/w/index.php?title=Zna%C4%8Dilnost&action=edit&redlink=1" class="new" title="Značilnost (stran ne obstaja)">značilnosti</a> <a href="/w/index.php?title=Supremum&action=edit&redlink=1" class="new" title="Supremum (stran ne obstaja)">najmanjše zgornje meje</a> realnih števil prav tako pomembno kot vprašanje o resničnosti <a href="/wiki/Georg_Wilhelm_Friedrich_Hegel" title="Georg Wilhelm Friedrich Hegel">Heglovih</a> temeljnih trditev o filozofiji narave. Vsak odgovor na takšno vprašanje bi bil nepreverljiv, nepovezan z izkustvom, in zaradi tega nesmiseln.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Gurevich je leta 1995 na ETH našel točen zapis o stavi. Prijateljska stava se je končala leta 1937. Za zmagovalca so proglasili Pólyo, pri čemer je bil <a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Gödel</a> drugačnega mišljenja. Čeprav je Weyl priznal poraz, tudi s Pólyevo odobritvijo ni mogel o tem objaviti oglas v letniku Nemškega matematičnega društva, kot je bilo navedeno v stavi. </p><p>Čez nekaj let se je Weyl odločil, da Brouwerjev intuicionizem preveč omejuje matematiko, kot so govorili tudi kritiki. »Krizni« članek je vznemiril Weylovega <a href="/w/index.php?title=Formalizem_(matematika)&action=edit&redlink=1" class="new" title="Formalizem (matematika) (stran ne obstaja)">formalističnega</a> učitelja Hilberta. V poznih 1920-ih je Weyl delno pomiril svoja stališča s Hilbertom. </p><p>Približno po letu 1928 se je Weyl verjetno odločil, da matematični intuicionizem ni združljiv z njegovim navdušenjem za <a href="/wiki/Edmund_Husserl" title="Edmund Husserl">Husserlovo</a> <a href="/wiki/Fenomenologija" title="Fenomenologija">fenomenološko</a> filozofijo, kot je mislil prej. V zadnjih desetletjih življenja je Weyl poudarjal razumevanje matematike kot »simbolično konstrukcijo« in prešel na stališče bližje ne samo Hilbertu, ampak tudi <a href="/wiki/Ernst_Cassirer" title="Ernst Cassirer">Cassirerju</a>. Weyl pa je sicer redko navajal Cassirerja. Pisal je le kratke članke in odlomke, ter pojasnjeval svoje stališče. </p> <div class="mw-heading mw-heading2"><h2 id="Glavna_dela">Glavna dela</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=4" title="Uredi razdelek: Glavna dela" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=4" title="Urejanje izvorne kode razdelka: Glavna dela"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Njegova glavna dela so: </p> <ul><li><i>Idee der Riemannflāche</i>, (1913),</li> <li><i>Das Kontinuum</i>, (1918),</li> <li><i>Gruppentheorie und Quantenmechanik</i>, (1928),</li> <li><i>Mind and Nature</i> (University of Pennsylvania Press, 1934),</li> <li><i>Elementary Theory of Invariants</i> (1935),</li> <li><i>Classical Groups: Their Invariants And Representations</i>, (Princeton 1939, <a href="/wiki/Posebno:ViriKnjig/0691057567" class="internal mw-magiclink-isbn">ISBN 0-691-05756-7</a>)</li> <li><i>Algebraic Theory of Numbers</i> (1940),</li> <li><i>Meromorphic Functions and Analytic Curves</i>, (Princeton University Press, Princeton 1943),</li> <li><i>Philosophy of Mathematics and Natural Science</i>, (Princeton University Press, Princeton 1949),</li> <li><i>Simmetry</i>, (Princeton University Press, Princeton 1952, <a href="/wiki/Posebno:ViriKnjig/0691023743" class="internal mw-magiclink-isbn">ISBN 0-691-02374-3</a>),</li> <li><i>Algebraic Theory of Numbers</i>, (Princeton University Press, Princeton 1959).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Priznanja">Priznanja</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=5" title="Uredi razdelek: Priznanja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=5" title="Urejanje izvorne kode razdelka: Priznanja"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Nagrade">Nagrade</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=6" title="Uredi razdelek: Nagrade" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=6" title="Urejanje izvorne kode razdelka: Nagrade"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Leta 1927 je za svoje delo na področju geometrije prejel <a href="/w/index.php?title=Nagrada_Loba%C4%8Devskega&action=edit&redlink=1" class="new" title="Nagrada Lobačevskega (stran ne obstaja)">nagrado Lobačevskega</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Poimenovanja">Poimenovanja</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=7" title="Uredi razdelek: Poimenovanja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=7" title="Urejanje izvorne kode razdelka: Poimenovanja"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Po njem se imenuje <a href="/wiki/Udarni_krater" title="Udarni krater">udarni</a> <a href="/wiki/Lunini_kraterji" title="Lunini kraterji">krater</a> <a href="/w/index.php?title=Weyl_(krater)&action=edit&redlink=1" class="new" title="Weyl (krater) (stran ne obstaja)">Weyl</a> na <a href="/wiki/Oddaljena_stran_Lune" title="Oddaljena stran Lune">oddaljeni strani</a> <a href="/wiki/Luna" title="Luna">Lune</a> in <a href="/wiki/Asteroid" title="Asteroid">asteroid</a> <a href="/wiki/Asteroidni_pas" title="Asteroidni pas">glavnega pasu</a> <a href="/w/index.php?title=32267_Hermannweyl&action=edit&redlink=1" class="new" title="32267 Hermannweyl (stran ne obstaja)">32267 Hermannweyl</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Sklici">Sklici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=8" title="Uredi razdelek: Sklici" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=8" title="Urejanje izvorne kode razdelka: Sklici"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r5453066">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-100{font-size:100%}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns dl,.mw-parser-output .refbegin-columns ol,.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li,.mw-parser-output .refbegin-columns dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="refbegin refbegin-100 refbegin-columns references-column-count references-column-count-4" style="column-count: 4;"> <div class="reflist columns references-column-width" style="column-width: 25em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;_1-0">1,0</a></sup> <sup><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&quot;_data-entity-id=&quot;Q19938912&quot;&gt;data.bnf.fr:_platforma_za_odprte_podatke&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2011.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&lt;/div&gt;_1-1">1,1</a></sup></span> <span class="reference-text"><span class="wikidata_cite citetype_Q36524 citetype_Q7094076 citetype_Q27031827 citetype_Q595971" data-entity-id="Q19938912">data.bnf.fr: platforma za odprte podatke<span class="wef_low_priority_links"> — 2011.</span></span><div style="display:none"><a href="https://www.wikidata.org/wiki/Track:Q193563" class="extiw" title="d:Track:Q193563">d:Track:Q193563</a><a href="https://www.wikidata.org/wiki/Track:Q19938912" class="extiw" title="d:Track:Q19938912">d:Track:Q19938912</a></div></span> </li> <li id="cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q35127&quot;_data-entity-id=&quot;Q547473&quot;&gt;MacTutor_History_of_Mathematics_archive&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_1994.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q547473]]&lt;/div&gt;-2"><span class="mw-cite-backlink"><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q35127&quot;_data-entity-id=&quot;Q547473&quot;&gt;MacTutor_History_of_Mathematics_archive&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_1994.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q547473]]&lt;/div&gt;_2-0">↑</a></span> <span class="reference-text"><span class="wikidata_cite citetype_Q35127" data-entity-id="Q547473">MacTutor History of Mathematics archive<span class="wef_low_priority_links"> — 1994.</span></span><div style="display:none"><a href="https://www.wikidata.org/wiki/Track:Q547473" class="extiw" title="d:Track:Q547473">d:Track:Q547473</a></div></span> </li> <li id="cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q615699&quot;_data-entity-id=&quot;Q5375741&quot;&gt;[http://www.britannica.com/biography/Hermann-Weyl_Encyclopædia_Britannica]&lt;span_class=&quot;wef_low_priority_links&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q5375741]]&lt;/div&gt;-3"><span class="mw-cite-backlink"><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q615699&quot;_data-entity-id=&quot;Q5375741&quot;&gt;[http://www.britannica.com/biography/Hermann-Weyl_Encyclopædia_Britannica]&lt;span_class=&quot;wef_low_priority_links&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q5375741]]&lt;/div&gt;_3-0">↑</a></span> <span class="reference-text"><span class="wikidata_cite citetype_Q615699" data-entity-id="Q5375741"><a rel="nofollow" class="external text" href="http://www.britannica.com/biography/Hermann-Weyl">Encyclopædia Britannica</a><span class="wef_low_priority_links"></span></span><div style="display:none"><a href="https://www.wikidata.org/wiki/Track:Q5375741" class="extiw" title="d:Track:Q5375741">d:Track:Q5375741</a></div></span> </li> <li id="cite_note-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;-4"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-0">4,0</a></sup> <sup><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-1">4,1</a></sup> <sup><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-2">4,2</a></sup> <sup><a href="#cite_ref-&lt;span_class=&quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&quot;_data-entity-id=&quot;Q36578&quot;&gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&lt;span_class=&quot;wef_low_priority_links&quot;&gt;_—_2012—2016.&lt;/span&gt;&lt;/span&gt;&lt;div_style=&quot;display:none&quot;&gt;[[d:Track:Q27302]][[d:Track:Q36578]]&lt;/div&gt;_4-3">4,3</a></sup></span> <span class="reference-text"><span class="wikidata_cite citetype_Q36524 citetype_Q17152639 citetype_Q1172284" data-entity-id="Q36578"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/118816624/">Record #118816624, Record #181399709</a> // Gemeinsame Normdatei<span class="wef_low_priority_links"> — 2012—2016.</span></span><div style="display:none"><a href="https://www.wikidata.org/wiki/Track:Q27302" class="extiw" title="d:Track:Q27302">d:Track:Q27302</a><a href="https://www.wikidata.org/wiki/Track:Q36578" class="extiw" title="d:Track:Q36578">d:Track:Q36578</a></div></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r5980307">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"»""«""›""‹"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite class="citation cs2">»An interview with Michael Atiyah«, <i><a href="/w/index.php?title=The_Mathematical_Intelligencer&action=edit&redlink=1" class="new" title="The Mathematical Intelligencer (stran ne obstaja)">The Mathematical Intelligencer</a></i>, <b>6</b> (1): 9–19, Marec 1984, <a href="/wiki/Doi_(identifikator)" class="mw-redirect" title="Doi (identifikator)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF03024202">10.1007/BF03024202</a>, <a href="/wiki/ISSN_(identifikator)" class="mw-redirect" title="ISSN (identifikator)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/0343-6993">0343-6993</a>, <a href="/wiki/S2CID_(identifikator)" class="mw-redirect" title="S2CID (identifikator)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:140298726">140298726</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=%C4%8Dlanek&rft.jtitle=The+Mathematical+Intelligencer&rft.atitle=An+interview+with+Michael+Atiyah&rft.volume=6&rft.issue=1&rft.pages=9-19&rft.date=1984-03&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A140298726%23id-name%3DS2CID&rft.issn=0343-6993&rft_id=info%3Adoi%2F10.1007%2FBF03024202&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Primerjaj Elsner, str. 3–15.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140115174358/http://genealogy.math.uni-bielefeld.de/genealogy/id.php?id=7373">»Hermann Claus Hugo Weyl«</a>. <i><a href="/wiki/Projekt_Matemati%C4%8Dna_genealogija" class="mw-redirect" title="Projekt Matematična genealogija">Projekt Matematična genealogija</a></i> (v angleščini). Arhivirano iz <a rel="nofollow" class="external text" href="http://genealogy.math.uni-bielefeld.de/genealogy/id.php?id=7373">prvotnega spletišča</a> dne 15. januarja 2014<span class="reference-accessdate">. Pridobljeno 16. aprila 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=neznano&rft.jtitle=Projekt+Matemati%C4%8Dna+genealogija&rft.atitle=Hermann+Claus+Hugo+Weyl&rft_id=http%3A%2F%2Fgenealogy.math.uni-bielefeld.de%2Fgenealogy%2Fid.php%3Fid%3D7373&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFSuhadolc2010"> Suhadolc (2010)</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFGurevich1995"> Gurevich (1995)</a>.</span> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Viri">Viri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=9" title="Uredi razdelek: Viri" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=9" title="Urejanje izvorne kode razdelka: Viri"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5453066"><div class="refbegin refbegin-100 refbegin-columns references-column-count references-column-count-1" style="column-count: 1;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFElsner2008" class="citation cs2">Elsner, Bernd (2008), <i>Die Abiturarbeit Hermann Weyls</i> (v <i>Christianeum</i>, Jg. 63, H. 1 izd.)</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=Die+Abiturarbeit+Hermann+Weyls&rft.edition=v+%27%27Christianeum%27%27%2C+Jg.+63%2C+H.+1&rft.date=2008&rft.aulast=Elsner&rft.aufirst=Bernd&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFGurevich1995" class="citation cs2">Gurevich, Yuri (1995), <a rel="nofollow" class="external text" href="http://research.microsoft.com/~gurevich/Opera/123.pdf">»Platonism, Constructivism and Computer Proofs vs Proofs by Hand«</a> <span class="cs1-format">(PDF)</span>, <i>Bulletin of the European Association of Theoretical Computer Science</i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=%C4%8Dlanek&rft.jtitle=Bulletin+of+the+European+Association+of+Theoretical+Computer+Science&rft.atitle=Platonism%2C+Constructivism+and+Computer+Proofs+vs+Proofs+by+Hand&rft.date=1995&rft.aulast=Gurevich&rft.aufirst=Yuri&rft_id=http%3A%2F%2Fresearch.microsoft.com%2F~gurevich%2FOpera%2F123.pdf&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFSuhadolc2010" class="citation cs2"><a href="/wiki/Anton_Suhadolc" title="Anton Suhadolc">Suhadolc, Anton</a> (2010), »O profesorju Josipu Plemlju«, <i><a href="/wiki/Obzornik_za_matematiko_in_fiziko" title="Obzornik za matematiko in fiziko">Obzornik za matematiko in fiziko</a></i>, <b>57</b> (2): 53–57</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=%C4%8Dlanek&rft.jtitle=Obzornik+za+matematiko+in+fiziko&rft.atitle=O+profesorju+Josipu+Plemlju&rft.volume=57&rft.issue=2&rft.pages=53-57&rft.date=2010&rft.aulast=Suhadolc&rft.aufirst=Anton&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFWheeler1986" class="citation cs2"><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler, John Archibald</a> (1986), <a rel="nofollow" class="external text" href="http://www.weylmann.com/wheeler.pdf">»Hermann Weyl and the Unity of Knowledge«</a> <span class="cs1-format">(PDF)</span>, <i><a href="/w/index.php?title=American_Scientist&action=edit&redlink=1" class="new" title="American Scientist (stran ne obstaja)">American Scientist</a></i>, <b>74</b> (4): 366–375</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=%C4%8Dlanek&rft.jtitle=American+Scientist&rft.atitle=Hermann+Weyl+and+the+Unity+of+Knowledge&rft.volume=74&rft.issue=4&rft.pages=366-375&rft.date=1986&rft.aulast=Wheeler&rft.aufirst=John+Archibald&rft_id=http%3A%2F%2Fwww.weylmann.com%2Fwheeler.pdf&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Zunanje_povezave">Zunanje povezave</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&veaction=edit&section=10" title="Uredi razdelek: Zunanje povezave" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=10" title="Urejanje izvorne kode razdelka: Zunanje povezave"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r5916282">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right plainlinks"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5911185"> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedijina zbirka ponuja več predstavnostnega gradiva o temi: <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Hermann_Weyl" class="extiw" title="commons:Category:Hermann Weyl">Hermann Weyl</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5916282"><div class="side-box metadata side-box-right plainlinks"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5911185"> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Wikiquote-logo-sl.svg/34px-Wikiquote-logo-sl.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Wikiquote-logo-sl.svg/51px-Wikiquote-logo-sl.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Wikiquote-logo-sl.svg/67px-Wikiquote-logo-sl.svg.png 2x" data-file-width="135" data-file-height="160" /></span></span></div> <div class="side-box-text plainlist"><a href="/wiki/Wikinavedek" title="Wikinavedek">Wikinavedek</a> vsebuje navedke o temi: <i><b><a href="https://sl.wikiquote.org/wiki/Special:Search/Hermann_Weyl" class="extiw" title="q:Special:Search/Hermann Weyl">Hermann Weyl</a></b></i></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://academictree.org/math/tree.php?pid=175048">Akademsko drevo Hermanna Weyla</a> na Math Tree <span class="languageicon">(angleško)</span></li> <li><a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Weyl.html">Stran o Hermannu Weylu</a> <a href="/w/index.php?title=Univerza_svetega_Andreja&action=edit&redlink=1" class="new" title="Univerza svetega Andreja (stran ne obstaja)">Univerze svetega Andreja</a> <span class="languageicon">(angleško)</span></li> <li><a rel="nofollow" class="external text" href="http://www.genealogy.ams.org/id.php?id=7373">Hermann Weyl</a> na <a href="/wiki/Projekt_Matemati%C4%8Dna_genealogija" class="mw-redirect" title="Projekt Matematična genealogija">Projektu Matematična genealogija</a> <span class="languageicon">(angleško)</span></li> <li><a href="/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah">Atiyah, Michael Francis</a> <a rel="nofollow" class="external text" href="http://www.nap.edu/readingroom/books/biomems/hweyl.html">Življenjepis Hermanna Weyla Nacionalne akademije znanosti ZDA</a> <span class="languageicon">(angleško)</span></li> <li><a rel="nofollow" class="external text" href="http://www.math.uni-goettingen.de/historisches/weyl.html">Kratek življenjepis Hermanna Weyla Matematične fakultete Univerze v Göttingenu</a> <span class="languageicon">(nemško)</span></li> <li><a href="/w/index.php?title=John_Lane_Bell&action=edit&redlink=1" class="new" title="John Lane Bell (stran ne obstaja)">Bell, John Lane</a>, <i><a rel="nofollow" class="external text" href="http://publish.uwo.ca/~jbell/Hermann%20Weyl.pdf">Hermann Weyl on intuition and the continuum</a></i></li> <li>Bell, John Lane, <i><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/weyl/">Hermann Weyl</a></i> v <a href="/w/index.php?title=Stanford_Encyclopedia_of_Philosophy&action=edit&redlink=1" class="new" title="Stanford Encyclopedia of Philosophy (stran ne obstaja)">Stanford Encyclopedia of Philosophy</a> <span class="languageicon">(angleško)</span></li> <li>Feferman, Solomon. <a rel="nofollow" class="external text" href="http://webcache.googleusercontent.com/search?q=cache:2aHbpRifP0AJ:math.stanford.edu/~feferman/papers/DasKontinuum.pdf">"Significance of Hermann Weyl's das Kontinuum"</a></li> <li>Straub, William O. <a rel="nofollow" class="external text" href="http://www.weylmann.com">Spletišče o Hermannu Weylu</a> <span class="languageicon">(angleško)</span></li></ul> <div role="navigation" class="navbox" aria-labelledby="Normativna_kontrola_frameless&#124;text-top&#124;10px&#124;alt=Uredite_to_na_Wikipodatkih&#124;link=https&#58;//www.wikidata.org/wiki/Q71029#identifiers&#124;class=noprint&#124;Uredite_to_na_Wikipodatkih" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Normativna_kontrola_frameless&#124;text-top&#124;10px&#124;alt=Uredite_to_na_Wikipodatkih&#124;link=https&#58;//www.wikidata.org/wiki/Q71029#identifiers&#124;class=noprint&#124;Uredite_to_na_Wikipodatkih" style="font-size:114%;margin:0 4em"><a href="/wiki/Wikipedija:Normativna_kontrola" title="Wikipedija:Normativna kontrola">Normativna kontrola</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q71029#identifiers" title="Uredite to na Wikipodatkih"><img alt="Uredite to na Wikipodatkih" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, 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(identifikator)">CONOR (Slovenija)</a> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://plus.cobiss.net/cobiss/si/sl/conor/17552739">1</a></span></li></ul></li> <li><a href="/wiki/CONOR_(identifikator)" class="mw-redirect" title="CONOR (identifikator)">CONOR (Srbija)</a> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://plus.cobiss.net/cobiss/sr/sr/conor/15222631">1</a></span></li></ul></li> <li><span class="nowrap"><a rel="nofollow" class="external text" href="https://www.worldcat.org/identities/containsVIAFID/64072393">WorldCat (via VIAF)</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Narodne knjižnice</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90088543">Norveška</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX820224">Španija</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12305695b">Francija</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12305695b">(data)</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058520419506706">Katalonija</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118816624">Nemčija</a></span> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/181399709">2</a></span></li></ul></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007515321705171">Izrael</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/names/n50018035">ZDA</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000254856&P_CON_LNG=ENG">Latvija</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00460689">Japonska</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=jn20000703396&CON_LNG=ENG">Češka republika</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35602647">Avstralija</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://librarian.nl.go.kr/LI/contents/L20101000000.do?id=KAC201426159">Koreja</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="http://katalog.nsk.hr/F/?func=direct&doc_number=000534250&local_base=nsk10">Hrvaška</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p072834242">Nizozemska</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="http://mak.bn.org.pl/cgi-bin/KHW/makwww.exe?BM=1&NU=1&IM=4&WI=9810670253505606">Poljska</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/auth/238852">Švedska</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Biografski slovarji</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118816624.html?language=en">Nemčija</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Znanstvene podatkovne baze</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA00815026?l=en">CiNii (Japonska)</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/182220">MathSciNet</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=7373">Mathematics Genealogy Project</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://www.scopus.com/authid/detail.uri?authorId=22990639300">Scopus author</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:weyl.hermann">zbMATH</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Drugo</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/5722/">Faceted Application of Subject Terminology</a></span></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://hls-dhs-dss.ch/fr/articles/031708">Zgodovinski leksikon Švice</a></span></li> <li><a href="/wiki/RERO_(identifikator)" class="mw-redirect" title="RERO (identifikator)">RERO (Švica)</a> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.rero.ch/02-A013099288">1</a></span></li></ul></li> <li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w61v5gjm">Social Networks and Archival Context</a></span></li> <li><a href="/wiki/SUDOC_(identifikator)" class="mw-redirect" title="SUDOC (identifikator)">SUDOC (Francija)</a> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/031921434">1</a></span></li></ul></li> <li><a href="/wiki/Trove_(identifikator)" class="mw-redirect" title="Trove (identifikator)">Trove (Avstralija)</a> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1010959">1</a></span></li></ul></li></ul> </div></td></tr></tbody></table></div> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐74cbd4458c‐5m76z Cached time: 20241210182719 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.845 seconds Real time usage: 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