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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Ensaluti</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Paĝoj por elsalutitaj redaktistoj <a href="/wiki/Helpo:Enkonduko" aria-label="Lernu pli pri redaktado"><span>Lernu pli</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/Speciala%C4%B5o:Miaj_kontribuoj" title="Listo de redaktoj faritaj el ĉi tiu IPa adreso [y]" accesskey="y"><span>Kontribuoj</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Mia_diskutpa%C4%9Do" title="Diskuto pri redaktoj sub tiu ĉi IP adreso [n]" accesskey="n"><span>Diskuto</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"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Retejo"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Enhavo" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Enhavo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">kaŝi</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">Komenco</div> </a> </li> <li id="toc-Vidu_ankaŭ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vidu_ankaŭ"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Vidu ankaŭ</span> </div> </a> <ul id="toc-Vidu_ankaŭ-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="Enhavo" 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="Ŝaltu la enhavtabelon" > <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">Ŝaltu la enhavtabelon</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">Skalara produto</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="Iru al artikolo en alia lingvo. Havebla en 70 lingvo" > <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-70" 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">70 lingvoj</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8C%A5%E1%88%8B_%E1%89%A5%E1%8B%9C%E1%89%B5" title="ጥላ ብዜት — amhara" lang="am" hreflang="am" data-title="ጥላ ብዜት" data-language-autonym="አማርኛ" data-language-local-name="amhara" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D8%AF%D8%A7%D8%A1_%D9%86%D9%82%D8%B7%D9%8A" title="جداء نقطي — araba" lang="ar" hreflang="ar" data-title="جداء نقطي" data-language-autonym="العربية" data-language-local-name="araba" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Productu_escalar" title="Productu escalar — asturia" lang="ast" hreflang="ast" data-title="Productu escalar" data-language-autonym="Asturianu" data-language-local-name="asturia" 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/Skalyar_hasil" title="Skalyar hasil — azerbajĝana" lang="az" hreflang="az" data-title="Skalyar hasil" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajĝana" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80_%D2%A1%D0%B0%D0%B1%D0%B0%D1%82%D0%BB%D0%B0%D0%BD%D0%B4%D1%8B%D2%A1" title="Скаляр ҡабатландыҡ — baŝkira" lang="ba" hreflang="ba" data-title="Скаляр ҡабатландыҡ" data-language-autonym="Башҡортса" data-language-local-name="baŝkira" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D1%8B_%D0%B7%D0%B4%D0%B0%D0%B1%D1%8B%D1%82%D0%B0%D0%BA" title="Скалярны здабытак — belorusa" lang="be" hreflang="be" data-title="Скалярны здабытак" data-language-autonym="Беларуская" data-language-local-name="belorusa" 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%A1%D0%BA%D0%B0%D0%BB%D0%B0%D1%80%D0%BD%D0%BE_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" title="Скаларно произведение — bulgara" lang="bg" hreflang="bg" data-title="Скаларно произведение" data-language-autonym="Български" data-language-local-name="bulgara" 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%A1%E0%A6%9F_%E0%A6%97%E0%A7%81%E0%A6%A3%E0%A6%A8" title="ডট গুণন — bengala" lang="bn" hreflang="bn" data-title="ডট গুণন" data-language-autonym="বাংলা" data-language-local-name="bengala" 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/Skalarni_proizvod" title="Skalarni proizvod — bosna" lang="bs" hreflang="bs" data-title="Skalarni proizvod" data-language-autonym="Bosanski" data-language-local-name="bosna" 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/Producte_escalar" title="Producte escalar — kataluna" lang="ca" hreflang="ca" data-title="Producte escalar" data-language-autonym="Català" data-language-local-name="kataluna" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%DB%8E%DA%A9%D8%AF%D8%A7%D9%86%DB%8C_%D9%86%D8%A7%D9%88%DB%95%DA%A9%DB%8C" title="لێکدانی ناوەکی — sorana" lang="ckb" hreflang="ckb" data-title="لێکدانی ناوەکی" data-language-autonym="کوردی" data-language-local-name="sorana" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Skal%C3%A1rn%C3%AD_sou%C4%8Din" title="Skalární součin — ĉeĥa" lang="cs" hreflang="cs" data-title="Skalární součin" data-language-autonym="Čeština" data-language-local-name="ĉeĥa" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BB%D0%B0_%D1%85%D1%83%D1%82%D0%BB%D0%B0%D0%B2" title="Скалярла хутлав — ĉuvaŝa" lang="cv" hreflang="cv" data-title="Скалярла хутлав" data-language-autonym="Чӑвашла" data-language-local-name="ĉuvaŝa" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Skalarprodukt" title="Skalarprodukt — dana" lang="da" hreflang="da" data-title="Skalarprodukt" data-language-autonym="Dansk" data-language-local-name="dana" 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/Skalarprodukt" title="Skalarprodukt — germana" lang="de" hreflang="de" data-title="Skalarprodukt" data-language-autonym="Deutsch" data-language-local-name="germana" 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%95%CF%83%CF%89%CF%84%CE%B5%CF%81%CE%B9%CE%BA%CF%8C_%CE%B3%CE%B9%CE%BD%CF%8C%CE%BC%CE%B5%CE%BD%CE%BF" title="Εσωτερικό γινόμενο — greka" lang="el" hreflang="el" data-title="Εσωτερικό γινόμενο" data-language-autonym="Ελληνικά" data-language-local-name="greka" 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/Dot_product" title="Dot product — angla" lang="en" hreflang="en" data-title="Dot product" data-language-autonym="English" data-language-local-name="angla" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Producto_escalar" title="Producto escalar — hispana" lang="es" hreflang="es" data-title="Producto escalar" data-language-autonym="Español" data-language-local-name="hispana" 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/Skalaarkorrutis" title="Skalaarkorrutis — estona" lang="et" hreflang="et" data-title="Skalaarkorrutis" data-language-autonym="Eesti" data-language-local-name="estona" 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/Biderketa_eskalar" title="Biderketa eskalar — eŭska" lang="eu" hreflang="eu" data-title="Biderketa eskalar" data-language-autonym="Euskara" data-language-local-name="eŭska" 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/%D8%B6%D8%B1%D8%A8_%D8%AF%D8%A7%D8%AE%D9%84%DB%8C" title="ضرب داخلی — persa" lang="fa" hreflang="fa" data-title="ضرب داخلی" data-language-autonym="فارسی" data-language-local-name="persa" 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/Pistetulo" title="Pistetulo — finna" lang="fi" hreflang="fi" data-title="Pistetulo" data-language-autonym="Suomi" data-language-local-name="finna" 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/Produit_scalaire" title="Produit scalaire — franca" lang="fr" hreflang="fr" data-title="Produit scalaire" data-language-autonym="Français" data-language-local-name="franca" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Produto_escalar" title="Produto escalar — galega" lang="gl" hreflang="gl" data-title="Produto escalar" data-language-autonym="Galego" data-language-local-name="galega" 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%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A1%D7%A7%D7%9C%D7%A8%D7%99%D7%AA" title="מכפלה סקלרית — hebrea" lang="he" hreflang="he" data-title="מכפלה סקלרית" data-language-autonym="עברית" data-language-local-name="hebrea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%A6%E0%A4%BF%E0%A4%B6_%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A4%A8%E0%A4%AB%E0%A4%B2" title="अदिश गुणनफल — hinda" lang="hi" hreflang="hi" data-title="अदिश गुणनफल" data-language-autonym="हिन्दी" data-language-local-name="hinda" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Skalarni_umno%C5%BEak" title="Skalarni umnožak — kroata" lang="hr" hreflang="hr" data-title="Skalarni umnožak" data-language-autonym="Hrvatski" data-language-local-name="kroata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Skal%C3%A1ris_szorzat" title="Skaláris szorzat — hungara" lang="hu" hreflang="hu" data-title="Skaláris szorzat" data-language-autonym="Magyar" data-language-local-name="hungara" 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%8D%D5%AF%D5%A1%D5%AC%D5%B5%D5%A1%D6%80_%D5%A1%D6%80%D5%BF%D5%A1%D5%A4%D6%80%D5%B5%D5%A1%D5%AC" title="Սկալյար արտադրյալ — armena" lang="hy" hreflang="hy" data-title="Սկալյար արտադրյալ" data-language-autonym="Հայերեն" data-language-local-name="armena" 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/Produk_dot" title="Produk dot — indonezia" lang="id" hreflang="id" data-title="Produk dot" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezia" 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/Prodotto_scalare" title="Prodotto scalare — itala" lang="it" hreflang="it" data-title="Prodotto scalare" data-language-autonym="Italiano" data-language-local-name="itala" 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%89%E3%83%83%E3%83%88%E7%A9%8D" title="ドット積 — japana" lang="ja" hreflang="ja" data-title="ドット積" data-language-autonym="日本語" data-language-local-name="japana" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%99%E1%83%90%E1%83%9A%E1%83%90%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%9C%E1%83%90%E1%83%9B%E1%83%A0%E1%83%90%E1%83%95%E1%83%9A%E1%83%98" title="სკალარული ნამრავლი — kartvela" lang="ka" hreflang="ka" data-title="სკალარული ნამრავლი" data-language-autonym="ქართული" data-language-local-name="kartvela" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80_%D0%BA%D3%A9%D0%B1%D0%B5%D0%B9%D1%82%D1%96%D0%BD%D0%B4%D1%96" title="Скаляр көбейтінді — kazaĥa" lang="kk" hreflang="kk" data-title="Скаляр көбейтінді" data-language-autonym="Қазақша" data-language-local-name="kazaĥa" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8A%A4%EC%B9%BC%EB%9D%BC%EA%B3%B1" title="스칼라곱 — korea" lang="ko" hreflang="ko" data-title="스칼라곱" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Productum_interius" title="Productum interius — latino" lang="la" hreflang="la" data-title="Productum interius" data-language-autonym="Latina" data-language-local-name="latino" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Skaliarin%C4%97_sandauga" title="Skaliarinė sandauga — litova" lang="lt" hreflang="lt" data-title="Skaliarinė sandauga" data-language-autonym="Lietuvių" data-language-local-name="litova" 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/Skal%C4%81rais_reizin%C4%81jums" title="Skalārais reizinājums — latva" lang="lv" hreflang="lv" data-title="Skalārais reizinājums" data-language-autonym="Latviešu" data-language-local-name="latva" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D0%B0%D1%80%D0%B5%D0%BD_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4" title="Скаларен производ — makedona" lang="mk" hreflang="mk" data-title="Скаларен производ" data-language-autonym="Македонски" data-language-local-name="makedona" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%82_%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A4%BE%E0%A4%95%E0%A4%BE%E0%A4%B0" title="बिंदू गुणाकार — marata" lang="mr" hreflang="mr" data-title="बिंदू गुणाकार" data-language-autonym="मराठी" data-language-local-name="marata" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hasil_darab_bintik" title="Hasil darab bintik — malaja" lang="ms" hreflang="ms" data-title="Hasil darab bintik" data-language-autonym="Bahasa Melayu" data-language-local-name="malaja" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Inwendig_product" title="Inwendig product — nederlanda" lang="nl" hreflang="nl" data-title="Inwendig product" data-language-autonym="Nederlands" data-language-local-name="nederlanda" 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/Indreprodukt" title="Indreprodukt — novnorvega" lang="nn" hreflang="nn" data-title="Indreprodukt" data-language-autonym="Norsk nynorsk" data-language-local-name="novnorvega" 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/Indreprodukt" title="Indreprodukt — dannorvega" lang="nb" hreflang="nb" data-title="Indreprodukt" data-language-autonym="Norsk bokmål" data-language-local-name="dannorvega" 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/Iloczyn_skalarny" title="Iloczyn skalarny — pola" lang="pl" hreflang="pl" data-title="Iloczyn skalarny" data-language-autonym="Polski" data-language-local-name="pola" 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/Prodot_%C3%ABscalar" title="Prodot ëscalar — Piedmontese" lang="pms" hreflang="pms" data-title="Prodot ëscalar" 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/Produto_escalar" title="Produto escalar — portugala" lang="pt" hreflang="pt" data-title="Produto escalar" data-language-autonym="Português" data-language-local-name="portugala" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Produs_scalar" title="Produs scalar — rumana" lang="ro" hreflang="ro" data-title="Produs scalar" data-language-autonym="Română" data-language-local-name="rumana" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" title="Скалярное произведение — rusa" lang="ru" hreflang="ru" data-title="Скалярное произведение" data-language-autonym="Русский" data-language-local-name="rusa" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" title="Скалярное произведение — jakuta" lang="sah" hreflang="sah" data-title="Скалярное произведение" data-language-autonym="Саха тыла" data-language-local-name="jakuta" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Dot_product" title="Dot product — skota" lang="sco" hreflang="sco" data-title="Dot product" data-language-autonym="Scots" data-language-local-name="skota" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Skalarni_proizvod_vektora" title="Skalarni proizvod vektora — serbo-Kroata" lang="sh" hreflang="sh" data-title="Skalarni proizvod vektora" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-Kroata" 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/Dot_product" title="Dot product — Simple English" lang="en-simple" hreflang="en-simple" data-title="Dot product" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Skal%C3%A1rny_s%C3%BA%C4%8Din" title="Skalárny súčin — slovaka" lang="sk" hreflang="sk" data-title="Skalárny súčin" data-language-autonym="Slovenčina" data-language-local-name="slovaka" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Skalarni_produkt" title="Skalarni produkt — slovena" lang="sl" hreflang="sl" data-title="Skalarni produkt" data-language-autonym="Slovenščina" data-language-local-name="slovena" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Prodhimi_skalar" title="Prodhimi skalar — albana" lang="sq" hreflang="sq" data-title="Prodhimi skalar" data-language-autonym="Shqip" data-language-local-name="albana" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D0%B0%D1%80%D0%BD%D0%B8_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B0" title="Скаларни производ вектора — serba" lang="sr" hreflang="sr" data-title="Скаларни производ вектора" data-language-autonym="Српски / srpski" data-language-local-name="serba" 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/Skal%C3%A4rprodukt" title="Skalärprodukt — sveda" lang="sv" hreflang="sv" data-title="Skalärprodukt" data-language-autonym="Svenska" data-language-local-name="sveda" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%81%E0%AE%B3%E0%AF%8D%E0%AE%B3%E0%AE%BF%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AF%86%E0%AE%B0%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B2%E0%AF%8D" title="புள்ளிப் பெருக்கல் — tamila" lang="ta" hreflang="ta" data-title="புள்ளிப் பெருக்கல்" data-language-autonym="தமிழ்" data-language-local-name="tamila" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9C%E0%B8%A5%E0%B8%84%E0%B8%B9%E0%B8%93%E0%B8%88%E0%B8%B8%E0%B8%94" title="ผลคูณจุด — taja" lang="th" hreflang="th" data-title="ผลคูณจุด" data-language-autonym="ไทย" data-language-local-name="taja" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Produktong_tuldok" title="Produktong tuldok — tagaloga" lang="tl" hreflang="tl" data-title="Produktong tuldok" data-language-autonym="Tagalog" data-language-local-name="tagaloga" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Nokta_%C3%A7arp%C4%B1m" title="Nokta çarpım — turka" lang="tr" hreflang="tr" data-title="Nokta çarpım" data-language-autonym="Türkçe" data-language-local-name="turka" 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/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80_%D1%82%D0%B0%D0%BF%D0%BA%D1%8B%D1%80%D1%87%D1%8B%D0%B3%D1%8B%D1%88" title="Скаляр тапкырчыгыш — tatara" lang="tt" hreflang="tt" data-title="Скаляр тапкырчыгыш" data-language-autonym="Татарча / tatarça" data-language-local-name="tatara" 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%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%B8%D0%B9_%D0%B4%D0%BE%D0%B1%D1%83%D1%82%D0%BE%D0%BA" title="Скалярний добуток — ukraina" lang="uk" hreflang="uk" data-title="Скалярний добуток" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%88%D9%88%D9%B9_%D9%BE%D8%B1%D9%88%DA%88%DA%A9%D9%B9" title="ڈوٹ پروڈکٹ — urduo" lang="ur" hreflang="ur" data-title="ڈوٹ پروڈکٹ" data-language-autonym="اردو" data-language-local-name="urduo" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Skalyar_ko%CA%BBpaytmasi" title="Skalyar koʻpaytmasi — uzbeka" lang="uz" hreflang="uz" data-title="Skalyar koʻpaytmasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeka" 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/T%C3%ADch_v%C3%B4_h%C6%B0%E1%BB%9Bng" title="Tích vô hướng — vjetnama" lang="vi" hreflang="vi" data-title="Tích vô hướng" data-language-autonym="Tiếng Việt" data-language-local-name="vjetnama" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B0%E9%87%8F%E7%A7%AF" title="数量积 — vua" lang="wuu" hreflang="wuu" data-title="数量积" data-language-autonym="吴语" data-language-local-name="vua" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%82%B9%E7%A7%AF" title="点积 — ĉina" lang="zh" hreflang="zh" data-title="点积" data-language-autonym="中文" data-language-local-name="ĉina" 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/%E9%BB%9E%E7%A9%8D" title="點積 — kantona" lang="yue" hreflang="yue" data-title="點積" data-language-autonym="粵語" data-language-local-name="kantona" 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/Q181365#sitelinks-wikipedia" title="Redakti interlingvajn ligilojn" class="wbc-editpage">Redakti ligilojn</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="Nomspacoj"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs 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ligilo</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Skalara_produto&action=info" title="Pli da informo pri ĉi tiu paĝo"><span>Informoj pri la paĝo</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:Citi&page=Skalara_produto&id=8451353&wpFormIdentifier=titleform" title="Informoj pri kiel citi ĉi tiun paĝon"><span>Citi ĉi tiun artikolon</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:UrlShortener&url=https%3A%2F%2Feo.wikipedia.org%2Fwiki%2FSkalara_produto"><span>Akiri mallongigitan URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:QrCode&url=https%3A%2F%2Feo.wikipedia.org%2Fwiki%2FSkalara_produto"><span>Elŝutu QR-kodon</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"> Presi/elporti </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=Speciala%C4%B5o:Libro&bookcmd=book_creator&referer=Skalara+produto"><span>Krei libron</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:DownloadAsPdf&page=Skalara_produto&action=show-download-screen"><span>Elŝuti kiel PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Skalara_produto&printable=yes" title="Presebla versio de tiu ĉi paĝo [p]" accesskey="p"><span>Presebla versio</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> En aliaj projektoj </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Scalar_product" hreflang="en"><span>Vikimedia Komunejo</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q181365" title="Ligilo al konektita datuma ero [g]" accesskey="g"><span>Ero en Vikidatumoj</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Paĝaj iloj"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspekto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspekto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">kaŝi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">El Vikipedio, la libera enciklopedio</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eo" dir="ltr"><dl><dd><i><b>Skalara produto</b> estas malsama ol <a href="/wiki/Skalara_multipliko" title="Skalara multipliko">skalara multipliko</a>.</i></dd></dl> <hr /> <p><b>Skalara produto</b> aŭ <b>punkta produto</b> de du <a href="/wiki/Vektoro" title="Vektoro">vektoroj</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 \mathbf {a} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:1.676ex;" alt="{\displaystyle \mathbf {a} }"></span> kaj <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 \mathbf {b} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {b} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13ebf4628a1adf07133a6009e4a78bdd990c6eb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.176ex;" alt="{\displaystyle \mathbf {b} }"></span> estas skribata kiel </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 \mathbf {a} \cdot \mathbf {b} \;,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mspace width="thickmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} \cdot \mathbf {b} \;,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df82e169d71752453537fd318be65c9d8c6efa48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.756ex; height:2.509ex;" alt="{\displaystyle \mathbf {a} \cdot \mathbf {b} \;,}"></span></dd></dl> <p>kaj ĝi estas </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 |\mathbf {a} ||\mathbf {b} |\cos \theta }"> <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"> <mi mathvariant="bold">a</mi> </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"> <mi mathvariant="bold">b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\mathbf {a} ||\mathbf {b} |\cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafc0150f3bcdf1cfe246c4a8e142a2a6e4244b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.348ex; height:2.843ex;" alt="{\displaystyle |\mathbf {a} ||\mathbf {b} |\cos \theta }"></span></dd></dl> <p>kie <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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> estas <a href="/wiki/Angulo" title="Angulo">angulo</a> inter la vektoroj <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 \mathbf {a} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:1.676ex;" alt="{\displaystyle \mathbf {a} }"></span> kaj <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 \mathbf {b} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">b</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {b} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3654ae7aa05aad4aa7a3432e5d4169dfb0be078" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.132ex; height:2.509ex;" alt="{\displaystyle \mathbf {b} ,}"></span> kaj <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 |\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"> <mi mathvariant="bold">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\mathbf {a} |}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e552f1e95bc5e98cf3af4168af6c1592e6328a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.593ex; height:2.843ex;" alt="{\displaystyle |\mathbf {a} |}"></span> kaj <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 |\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"> <mi mathvariant="bold">b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\mathbf {b} |}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3deb5b40fd7f2fbf5f1b636c8fc88c58a1838adc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.779ex; height:2.843ex;" alt="{\displaystyle |\mathbf {b} |}"></span> estas la <a href="/wiki/Normo_(matematiko)" title="Normo (matematiko)">normoj</a> (aŭ <a href="/wiki/Absoluta_valoro" title="Absoluta valoro">absolutaj valoroj</a>) de tiuj konsiderataj vektoroj. La rezulto estas <a href="/wiki/Reela_nombro" class="mw-redirect" title="Reela nombro">reela nombro</a>. </p><p>Se ambaŭ vektoroj estas ne nulaj, <i>skalara produto</i> estas pozitiva se <i>θ<π/2</i>, egalas al 0 se <i>θ=π/2</i>, kaj negativa se <i>θ>π/2</i> (ĉiam <i>0≤θ≤π</i>). </p><p><i>Skalara produto</i> estas <a href="/wiki/Funkcio" class="mw-disambig" title="Funkcio">funkcio</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 f:E\times E\rightarrow R\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>E</mi> <mo>×</mo> <mi>E</mi> <mo stretchy="false">→</mo> <mi>R</mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:E\times E\rightarrow R\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c822770f701271d7084e1e23436eb464d05e527f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.019ex; height:2.509ex;" alt="{\displaystyle f:E\times E\rightarrow R\,,}"></span> kie <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 E\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f37dd4367bedcbfabd67d904fd86812ae4897354" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.356ex; height:2.176ex;" alt="{\displaystyle E\ }"></span> estas <a href="/wiki/Reela_nombro" class="mw-redirect" title="Reela nombro">reela</a> <a href="/wiki/Vektorspaco" class="mw-redirect" title="Vektorspaco">vektor-spaco</a> kaj por kiu validas ĉi tiujn proprecojn : </p> <ul><li><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 \forall x\in E:f(x,x)\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>E</mi> <mo>:</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x\in E:f(x,x)\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76a6bfed360b042417aa20903ee7c322d9bb0b88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.218ex; height:2.843ex;" alt="{\displaystyle \forall x\in E:f(x,x)\geq 0}"></span></li> <li><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 \forall x\in E:f(x,x)=0\iff x=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>E</mi> <mo>:</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⟺</mo> <mspace width="thickmathspace" /> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x\in E:f(x,x)=0\iff x=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbcf0cccbad4519ae10c9f15e6a9710cb74e63d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.706ex; height:2.843ex;" alt="{\displaystyle \forall x\in E:f(x,x)=0\iff x=0}"></span></li> <li><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 \forall (x,y)\in E^{2}:f(x,y)=f(y,x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>:</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall (x,y)\in E^{2}:f(x,y)=f(y,x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f878c9ad15cd3efae40ef6699d568a490ad5481" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.559ex; height:3.176ex;" alt="{\displaystyle \forall (x,y)\in E^{2}:f(x,y)=f(y,x)}"></span></li> <li><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 \forall (x,y,z)\in E^{3},\forall (\alpha ,\beta )\in R:f(\alpha x+\beta y\;,\,z)=\alpha f(x,z)+\beta f(y,z)\;.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>R</mi> <mo>:</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mi>x</mi> <mo>+</mo> <mi>β</mi> <mi>y</mi> <mspace width="thickmathspace" /> <mo>,</mo> <mspace width="thinmathspace" /> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>α</mi> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>β</mi> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall (x,y,z)\in E^{3},\forall (\alpha ,\beta )\in R:f(\alpha x+\beta y\;,\,z)=\alpha f(x,z)+\beta f(y,z)\;.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a264067f7adf63c8171e154a39a24377662e8f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:66.306ex; height:3.176ex;" alt="{\displaystyle \forall (x,y,z)\in E^{3},\forall (\alpha ,\beta )\in R:f(\alpha x+\beta y\;,\,z)=\alpha f(x,z)+\beta f(y,z)\;.}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Vidu_ankaŭ"><span id="Vidu_anka.C5.AD"></span>Vidu ankaŭ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Skalara_produto&veaction=edit&section=1" title="Redakti sekcion: Vidu ankaŭ" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Skalara_produto&action=edit&section=1" title="Redakti la fontkodo de la sekcio: Vidu ankaŭ"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Produto_de_vektoroj" class="mw-redirect" title="Produto de vektoroj">Produto de vektoroj</a></li> <li><a href="/wiki/Vektora_produto" title="Vektora produto">Vektora produto</a> (aŭ <i>kruca produto</i>)</li> <li><a href="/wiki/Skalara_projekcio" title="Skalara projekcio">Skalara projekcio</a></li> <li><a href="/wiki/Vektora_projekcio" title="Vektora projekcio">Vektora projekcio</a></li></ul> <div class="noprint" id="aliaj_projektoj" style="float: right; 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