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Hermann Weyl - Wikipedija, prosta enciklopedija

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class="vector-menu 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 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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&amp;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&amp;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&amp;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&amp;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&amp;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&amp;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&amp;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&amp;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&amp;page=Hermann_Weyl&amp;id=6230553&amp;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&amp;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&amp;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&amp;bookcmd=book_creator&amp;referer=Hermann+Weyl"><span>Ustvari e-knjigo</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a 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dir="ltr"><style data-mw-deduplicate="TemplateStyles:r5913888">.mw-parser-output .infobox{border:1px solid #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 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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 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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-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&amp;quot;_data-entity-id=&amp;quot;Q19938912&amp;quot;&amp;gt;data.bnf.fr:_platforma_za_odprte_podatke&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2011.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;&#91;&#91;d:Track:Q193563&#93;&#93;&#91;&#91;d:Track:Q19938912&#93;&#93;&amp;lt;/div&amp;gt;_1-1" class="reference"><a 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href="#cite_note-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&amp;quot;_data-entity-id=&amp;quot;Q36578&amp;quot;&amp;gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2012—2016.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q27302]][[d:Track:Q36578]]&amp;lt;/div&amp;gt;-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</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>&#160;<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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;redlink=1" class="new" title="Weylov kriterij (stran ne obstaja)">Weylov kriterij</a></li><li><a href="/w/index.php?title=Weylov_postulat&amp;action=edit&amp;redlink=1" class="new" title="Weylov postulat (stran ne obstaja)">Weylov postulat</a></li><li><a href="/w/index.php?title=Weylov_skalar&amp;action=edit&amp;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&amp;action=edit&amp;redlink=1" class="new" title="Weylov tenzor (stran ne obstaja)">Weylov tenzor</a></li><li><a href="/w/index.php?title=Weylova_algebra&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;redlink=1" class="new" title="Weylova grupa (stran ne obstaja)">Weylova grupa</a></li><li><a href="/w/index.php?title=Weylova_polkovina&amp;action=edit&amp;redlink=1" class="new" title="Weylova polkovina (stran ne obstaja)">Weylova polkovina</a></li><li><a href="/w/index.php?title=Weylova_transformacija&amp;action=edit&amp;redlink=1" class="new" title="Weylova transformacija (stran ne obstaja)">Weylova transformacija</a></li><li><a href="/w/index.php?title=Weylova_vsota&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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)&amp;action=edit&amp;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">&#91;</span>5<span class="cite-bracket">&#93;</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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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">&#91;</span>6<span class="cite-bracket">&#93;</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">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup> Leta 1910 je <a href="/w/index.php?title=Habilitacija&amp;action=edit&amp;redlink=1" class="new" title="Habilitacija (stran ne obstaja)">habilitiral</a> v <a href="/w/index.php?title=Privatni_docent&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;redlink=1" class="new" title="Aditivna teorija števil (stran ne obstaja)">aditivno teorijo števil</a> (<a href="/w/index.php?title=Weylova_vsota&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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,«&#160;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&amp;action=edit&amp;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&amp;action=edit&amp;redlink=1" class="new" title="Alexander Weinstein (stran ne obstaja)">Weinstein</a>, <a href="/w/index.php?title=Ernst_Max_Mohr&amp;action=edit&amp;redlink=1" class="new" title="Ernst Max Mohr (stran ne obstaja)">Mohr</a>, <a href="/w/index.php?title=Saunders_Mac_Lane&amp;action=edit&amp;redlink=1" class="new" title="Saunders Mac Lane (stran ne obstaja)">Mac Lane</a> in <a href="/w/index.php?title=Gerhard_Gentzen&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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">&#91;</span>8<span class="cite-bracket">&#93;</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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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.«&#160;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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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> &gt; 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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>&#x2212;<!-- − --></mo> <mo stretchy="false">(</mo> <mo>&#x2212;<!-- − --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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>&#x2212;<!-- − --></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>&#x2208;<!-- ∈ --></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>&#x2212;<!-- − --></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">&#x2192;<!-- → --></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>&#x2212;<!-- − --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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>&#x2212;<!-- − --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2212;<!-- − --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2212;<!-- − --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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&amp;action=edit&amp;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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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&amp;action=edit&amp;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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>&#x2265;<!-- ≥ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">&#x27FA;<!-- ⟺ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo>&#x2260;<!-- ≠ --></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">&#x2192;<!-- → --></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>&#x03BB;<!-- 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>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo>,</mo> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>&#x2265;<!-- ≥ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mi>&#x03BB;<!-- λ --></mi> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>&#x2265;<!-- ≥ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mi>&#x03BB;<!-- λ --></mi> <mo>&#x2212;<!-- − --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>&#x2264;<!-- ≤ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>&#x2264;<!-- ≤ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>&#x2264;<!-- ≤ --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>&#x03BB;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>&#x2264;<!-- ≤ --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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>&#x03D5;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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>&#x2061;<!-- ⁡ --></mo> <mi>&#x03D5;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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>&#x03D5;<!-- ϕ --></mi> <mo>=</mo> <mi>&#x03C0;<!-- 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>&#x2061;<!-- ⁡ --></mo> <mi>&#x03D5;<!-- 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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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">&#x2192;<!-- → --></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.«&#160;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.«&#160;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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>&#x2212;<!-- − --></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>&#x2212;<!-- − --></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>&#x03C4;<!-- 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>&#x2208;<!-- ∈ --></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>&#x03C4;<!-- 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">&#x00AF;<!-- ¯ --></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">&#x00AF;<!-- ¯ --></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">&#x00AF;<!-- ¯ --></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">&#x00AF;<!-- ¯ --></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>&#x2212;<!-- − --></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">&#x00AF;<!-- ¯ --></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>&#x2212;<!-- − --></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">&#x00AF;<!-- ¯ --></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>&#x2212;<!-- − --></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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;redlink=1" class="new" title="Značilnost (stran ne obstaja)">značilnosti</a> <a href="/w/index.php?title=Supremum&amp;action=edit&amp;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">&#91;</span>9<span class="cite-bracket">&#93;</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«&#160;članek je vznemiril Weylovega <a href="/w/index.php?title=Formalizem_(matematika)&amp;action=edit&amp;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«&#160;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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)&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&amp;quot;_data-entity-id=&amp;quot;Q19938912&amp;quot;&amp;gt;data.bnf.fr:_platforma_za_odprte_podatke&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2011.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;&#91;&#91;d:Track:Q193563&#93;&#93;&#91;&#91;d:Track:Q19938912&#93;&#93;&amp;lt;/div&amp;gt;-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&amp;quot;_data-entity-id=&amp;quot;Q19938912&amp;quot;&amp;gt;data.bnf.fr:_platforma_za_odprte_podatke&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2011.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&amp;lt;/div&amp;gt;_1-0">1,0</a></sup> <sup><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q7094076_citetype_Q27031827_citetype_Q595971&amp;quot;_data-entity-id=&amp;quot;Q19938912&amp;quot;&amp;gt;data.bnf.fr:_platforma_za_odprte_podatke&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2011.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q193563]][[d:Track:Q19938912]]&amp;lt;/div&amp;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-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q35127&amp;quot;_data-entity-id=&amp;quot;Q547473&amp;quot;&amp;gt;MacTutor_History_of_Mathematics_archive&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_1994.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;&#91;&#91;d:Track:Q547473&#93;&#93;&amp;lt;/div&amp;gt;-2"><span class="mw-cite-backlink"><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q35127&amp;quot;_data-entity-id=&amp;quot;Q547473&amp;quot;&amp;gt;MacTutor_History_of_Mathematics_archive&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_1994.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q547473]]&amp;lt;/div&amp;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-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q615699&amp;quot;_data-entity-id=&amp;quot;Q5375741&amp;quot;&amp;gt;&#91;http&#58;//www.britannica.com/biography/Hermann-Weyl_Encyclopædia_Britannica&#93;&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;&#91;&#91;d:Track:Q5375741&#93;&#93;&amp;lt;/div&amp;gt;-3"><span class="mw-cite-backlink"><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q615699&amp;quot;_data-entity-id=&amp;quot;Q5375741&amp;quot;&amp;gt;[http://www.britannica.com/biography/Hermann-Weyl_Encyclopædia_Britannica]&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q5375741]]&amp;lt;/div&amp;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-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&amp;quot;_data-entity-id=&amp;quot;Q36578&amp;quot;&amp;gt;&#91;http&#58;//d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709&#93;_//_Gemeinsame_Normdatei&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2012—2016.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;&#91;&#91;d:Track:Q27302&#93;&#93;&#91;&#91;d:Track:Q36578&#93;&#93;&amp;lt;/div&amp;gt;-4"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&amp;quot;_data-entity-id=&amp;quot;Q36578&amp;quot;&amp;gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2012—2016.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q27302]][[d:Track:Q36578]]&amp;lt;/div&amp;gt;_4-0">4,0</a></sup> <sup><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&amp;quot;_data-entity-id=&amp;quot;Q36578&amp;quot;&amp;gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2012—2016.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q27302]][[d:Track:Q36578]]&amp;lt;/div&amp;gt;_4-1">4,1</a></sup> <sup><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&amp;quot;_data-entity-id=&amp;quot;Q36578&amp;quot;&amp;gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2012—2016.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q27302]][[d:Track:Q36578]]&amp;lt;/div&amp;gt;_4-2">4,2</a></sup> <sup><a href="#cite_ref-&amp;lt;span_class=&amp;quot;wikidata_cite_citetype_Q36524_citetype_Q17152639_citetype_Q1172284&amp;quot;_data-entity-id=&amp;quot;Q36578&amp;quot;&amp;gt;[http://d-nb.info/gnd/118816624/_Record_#118816624,_Record_#181399709]_//_Gemeinsame_Normdatei&amp;lt;span_class=&amp;quot;wef_low_priority_links&amp;quot;&amp;gt;_—_2012—2016.&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;div_style=&amp;quot;display:none&amp;quot;&amp;gt;[[d:Track:Q27302]][[d:Track:Q36578]]&amp;lt;/div&amp;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&amp;action=edit&amp;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>&#160;<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>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:140298726">140298726</a></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=%C4%8Dlanek&amp;rft.jtitle=The+Mathematical+Intelligencer&amp;rft.atitle=An+interview+with+Michael+Atiyah&amp;rft.volume=6&amp;rft.issue=1&amp;rft.pages=9-19&amp;rft.date=1984-03&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A140298726%23id-name%3DS2CID&amp;rft.issn=0343-6993&amp;rft_id=info%3Adoi%2F10.1007%2FBF03024202&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=neznano&amp;rft.jtitle=Projekt+Matemati%C4%8Dna+genealogija&amp;rft.atitle=Hermann+Claus+Hugo+Weyl&amp;rft_id=http%3A%2F%2Fgenealogy.math.uni-bielefeld.de%2Fgenealogy%2Fid.php%3Fid%3D7373&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&#160;izd.)</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=knjiga&amp;rft.btitle=Die+Abiturarbeit+Hermann+Weyls&amp;rft.edition=v+%27%27Christianeum%27%27%2C+Jg.+63%2C+H.+1&amp;rft.date=2008&amp;rft.aulast=Elsner&amp;rft.aufirst=Bernd&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=%C4%8Dlanek&amp;rft.jtitle=Bulletin+of+the+European+Association+of+Theoretical+Computer+Science&amp;rft.atitle=Platonism%2C+Constructivism+and+Computer+Proofs+vs+Proofs+by+Hand&amp;rft.date=1995&amp;rft.aulast=Gurevich&amp;rft.aufirst=Yuri&amp;rft_id=http%3A%2F%2Fresearch.microsoft.com%2F~gurevich%2FOpera%2F123.pdf&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=%C4%8Dlanek&amp;rft.jtitle=Obzornik+za+matematiko+in+fiziko&amp;rft.atitle=O+profesorju+Josipu+Plemlju&amp;rft.volume=57&amp;rft.issue=2&amp;rft.pages=53-57&amp;rft.date=2010&amp;rft.aulast=Suhadolc&amp;rft.aufirst=Anton&amp;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&amp;action=edit&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=%C4%8Dlanek&amp;rft.jtitle=American+Scientist&amp;rft.atitle=Hermann+Weyl+and+the+Unity+of+Knowledge&amp;rft.volume=74&amp;rft.issue=4&amp;rft.pages=366-375&amp;rft.date=1986&amp;rft.aulast=Wheeler&amp;rft.aufirst=John+Archibald&amp;rft_id=http%3A%2F%2Fwww.weylmann.com%2Fwheeler.pdf&amp;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&amp;veaction=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;#124;text-top&amp;#124;10px&amp;#124;alt=Uredite_to_na_Wikipodatkih&amp;#124;link=https&amp;#58;//www.wikidata.org/wiki/Q71029#identifiers&amp;#124;class=noprint&amp;#124;Uredite_to_na_Wikipodatkih" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" 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