CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-disabled skin-theme-clientpref-day vector-toc-available" lang="lt" dir="ltr"> <head> <meta charset="UTF-8"> <title>Vektorinė erdvė – Vikipedija</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-disabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )ltwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t."," \t,"],"wgDigitTransformTable":["",""], "wgDefaultDateFormat":"dmy","wgMonthNames":["","sausio","vasario","kovo","balandžio","gegužės","birželio","liepos","rugpjūčio","rugsėjo","spalio","lapkričio","gruodžio"],"wgRequestId":"ea3d58b6-58fc-44ad-b2ab-33c4f2629bb8","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Vektorinė_erdvė","wgTitle":"Vektorinė erdvė","wgCurRevisionId":7178995,"wgRevisionId":7178995,"wgArticleId":157942,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Vektoriai"],"wgPageViewLanguage":"lt","wgPageContentLanguage":"lt","wgPageContentModel":"wikitext","wgRelevantPageName":"Vektorinė_erdvė","wgRelevantArticleId":157942,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0, "wgVisualEditor":{"pageLanguageCode":"lt","pageLanguageDir":"ltr","pageVariantFallbacks":"lt"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":6000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q125977","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false,"wgSiteNoticeId":"2.5"};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready" ,"user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready","ext.dismissableSiteNotice.styles":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints", "ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking","ext.dismissableSiteNotice"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=lt&modules=ext.cite.styles%7Cext.dismissableSiteNotice.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=lt&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=lt&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Vector_space_illust.svg/1200px-Vector_space_illust.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1467"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Vector_space_illust.svg/800px-Vector_space_illust.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="978"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Vector_space_illust.svg/640px-Vector_space_illust.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="782"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Vektorinė erdvė – Vikipedija"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//lt.m.wikipedia.org/wiki/Vektorin%C4%97_erdv%C4%97"> <link rel="alternate" type="application/x-wiki" title="Keisti" href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Vikipedija (lt)"> <link rel="EditURI" type="application/rsd+xml" href="//lt.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://lt.wikipedia.org/wiki/Vektorin%C4%97_erdv%C4%97"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.lt"> <link rel="alternate" type="application/atom+xml" title="Vikipedija Atom prenumerata" href="/w/index.php?title=Specialus:Naujausi_keitimai&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Vektorinė_erdvė rootpage-Vektorinė_erdvė skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Pereiti prie turinio</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Pagrindinis meniu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Pagrindinis meniu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Pagrindinis meniu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">paslėpti</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Naršymas </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Pagrindinis_puslapis" title="Eiti į pradinį puslapį [z]" accesskey="z"><span>Pagrindinis puslapis</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Vikipedija:Bendruomen%C4%97" title="Apie projektą, ką galima daryti, kur ką rasti"><span>Bendruomenės puslapis</span></a></li><li id="n-forumas" class="mw-list-item"><a href="/wiki/Vikipedija:Forumas"><span>Forumas</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Specialus:Naujausi_keitimai" title="Paskutinių keitimų sąrašas viki projekte [r]" accesskey="r"><span>Naujausi keitimai</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Specialus:Atsitiktinis_puslapis" title="Įkelti atsitiktinį puslapį [x]" accesskey="x"><span>Atsitiktinis straipsnis</span></a></li><li id="n-pagalba" class="mw-list-item"><a href="/wiki/Pagalba:Turinys"><span>Pagalba</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Pagrindinis_puslapis" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Vikipedija" src="/static/images/mobile/copyright/wikipedia-wordmark-lt.svg" style="width: 7.5em; height: 1.375em;"> <img class="mw-logo-tagline" alt="Laisvoji enciklopedija" src="/static/images/mobile/copyright/wikipedia-tagline-lt.svg" width="119" height="13" style="width: 7.4375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Specialus:Paie%C5%A1ka" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Ieškoti lietuviškame wiki [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Paieška</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Ieškoti Vikipedijoje" aria-label="Ieškoti Vikipedijoje" autocapitalize="sentences" title="Ieškoti lietuviškame wiki [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Specialus:Paieška"> </div> <button class="cdx-button cdx-search-input__end-button">Paieška</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Asmeniniai įrankiai"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Išvaizda"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Išvaizda" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Išvaizda</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_lt.wikipedia.org&uselang=lt" class=""><span>Parama</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Specialus:Sukurti_paskyr%C4%85&returnto=Vektorin%C4%97+erdv%C4%97" title="Skatiname susikurti paskyrą ir prisijungti, tačiau, tai nėra privaloma" class=""><span>Sukurti paskyrą</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Specialus:Prisijungimas&returnto=Vektorin%C4%97+erdv%C4%97" title="Rekomenduojame prisijungti, nors tai nėra privaloma [o]" accesskey="o" class=""><span>Prisijungti</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Daugiau parametrų" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Asmeniniai įrankiai" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Asmeniniai įrankiai</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Naudotojo meniu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_lt.wikipedia.org&uselang=lt"><span>Parama</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Specialus:Sukurti_paskyr%C4%85&returnto=Vektorin%C4%97+erdv%C4%97" title="Skatiname susikurti paskyrą ir prisijungti, tačiau, tai nėra privaloma"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Sukurti paskyrą</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Specialus:Prisijungimas&returnto=Vektorin%C4%97+erdv%C4%97" title="Rekomenduojame prisijungti, nors tai nėra privaloma [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Prisijungti</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"> Pages for logged out editors <a href="/wiki/Pagalba:Introduction" aria-label="Learn more about editing"><span>sužinoti daugiau</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/Specialus:Mano_ind%C4%97lis" title="Keitimų sąrašas, padarytų iš šio IP adreso [y]" accesskey="y"><span>Indėlis</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Specialus:Mano_aptarimas" title="Pakeitimų aptarimas, darytus naudojant šį IP adresą [n]" accesskey="n"><span>Šio IP aptarimų puslapis</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 id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Epaslėpti\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"sitenotice\" lang=\"lt\" dir=\"ltr\"\u003E\u003Cp\u003EŠios \u003Ca href=\"/wiki/Vikipedija:Savait%C4%97s_iniciatyva\" class=\"mw-redirect\" title=\"Vikipedija:Savaitės iniciatyva\"\u003Esavaitės iniciatyva\u003C/a\u003E: \u003Cb\u003ENobelio premijos laureatai\u003C/b\u003E. Kviečiame prisidėti!\n\u003C/p\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></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="Site"> <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="Turinys" 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">Turinys</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">paslėpti</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">Pradžia</div> </a> </li> <li id="toc-Formalus_apibrėžimas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formalus_apibrėžimas"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Formalus apibrėžimas</span> </div> </a> <ul id="toc-Formalus_apibrėžimas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elementarios_savybės" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Elementarios_savybės"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Elementarios savybės</span> </div> </a> <ul id="toc-Elementarios_savybės-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Šaltiniai" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Šaltiniai"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Šaltiniai</span> </div> </a> <ul id="toc-Šaltiniai-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="Turinys" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">Vektorinė erdvė</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="Go to an article in another language. Available in 77 languages" > <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-77" 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">77 kalbų</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Vektorruimte" title="Vektorruimte – afrikanų" lang="af" hreflang="af" data-title="Vektorruimte" data-language-autonym="Afrikaans" data-language-local-name="afrikanų" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7%D8%A1_%D9%85%D8%AA%D8%AC%D9%87%D9%8A" title="فضاء متجهي – arabų" lang="ar" hreflang="ar" data-title="فضاء متجهي" data-language-autonym="العربية" data-language-local-name="arabų" 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/Espaciu_vectorial" title="Espaciu vectorial – asturianų" lang="ast" hreflang="ast" data-title="Espaciu vectorial" data-language-autonym="Asturianu" data-language-local-name="asturianų" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BB%D1%8B_%D0%B0%D1%80%D0%B0%D1%83%D1%8B%D2%A1" title="Векторлы арауыҡ – baškirų" lang="ba" hreflang="ba" data-title="Векторлы арауыҡ" data-language-autonym="Башҡортса" data-language-local-name="baškirų" 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%92%D0%B5%D0%BA%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%BF%D1%80%D0%B0%D1%81%D1%82%D0%BE%D1%80%D0%B0" title="Вектарная прастора – baltarusių" lang="be" hreflang="be" data-title="Вектарная прастора" data-language-autonym="Беларуская" data-language-local-name="baltarusių" 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%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Линейно пространство – bulgarų" lang="bg" hreflang="bg" data-title="Линейно пространство" data-language-autonym="Български" data-language-local-name="bulgarų" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%95%E0%A5%8D%E0%A4%9F%E0%A4%B0_%E0%A4%B8%E0%A5%8D%E0%A4%AA%E0%A5%87%E0%A4%B8" title="वेक्टर स्पेस – Bhojpuri" lang="bh" hreflang="bh" data-title="वेक्टर स्पेस" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%A6%E0%A6%BF%E0%A6%95_%E0%A6%B0%E0%A6%BE%E0%A6%B6%E0%A6%BF%E0%A6%B0_%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="সদিক রাশির বীজগণিত – bengalų" lang="bn" hreflang="bn" data-title="সদিক রাশির বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="bengalų" 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/Vektorski_prostor" title="Vektorski prostor – bosnių" lang="bs" hreflang="bs" data-title="Vektorski prostor" data-language-autonym="Bosanski" data-language-local-name="bosnių" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle mw-list-item" title="pavyzdinis straipsnis"><a href="https://ca.wikipedia.org/wiki/Espai_vectorial" title="Espai vectorial – katalonų" lang="ca" hreflang="ca" data-title="Espai vectorial" data-language-autonym="Català" data-language-local-name="katalonų" 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/%D8%A8%DB%86%D8%B4%D8%A7%DB%8C%DB%8C%DB%8C_%D8%A6%D8%A7%DA%95%D8%A7%D8%B3%D8%AA%DB%95%D8%A8%DA%95%DB%95%DA%A9%D8%A7%D9%86" title="بۆشاییی ئاڕاستەبڕەکان – soranių kurdų" lang="ckb" hreflang="ckb" data-title="بۆشاییی ئاڕاستەبڕەکان" data-language-autonym="کوردی" data-language-local-name="soranių kurdų" 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/Vektorov%C3%BD_prostor" title="Vektorový prostor – čekų" lang="cs" hreflang="cs" data-title="Vektorový prostor" data-language-autonym="Čeština" data-language-local-name="čekų" 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%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BB%D0%B0_%D1%83%C3%A7%D0%BB%C4%83%D1%85" title="Векторла уçлăх – čiuvašų" lang="cv" hreflang="cv" data-title="Векторла уçлăх" data-language-autonym="Чӑвашла" data-language-local-name="čiuvašų" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Gofod_fector" title="Gofod fector – valų" lang="cy" hreflang="cy" data-title="Gofod fector" data-language-autonym="Cymraeg" data-language-local-name="valų" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Vektorrum" title="Vektorrum – danų" lang="da" hreflang="da" data-title="Vektorrum" data-language-autonym="Dansk" data-language-local-name="danų" 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/Vektorraum" title="Vektorraum – vokiečių" lang="de" hreflang="de" data-title="Vektorraum" data-language-autonym="Deutsch" data-language-local-name="vokiečių" 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%94%CE%B9%CE%B1%CE%BD%CF%85%CF%83%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CF%8C%CF%82_%CF%87%CF%8E%CF%81%CE%BF%CF%82" title="Διανυσματικός χώρος – graikų" lang="el" hreflang="el" data-title="Διανυσματικός χώρος" data-language-autonym="Ελληνικά" data-language-local-name="graikų" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="vertingas straipsnis"><a href="https://en.wikipedia.org/wiki/Vector_space" title="Vector space – anglų" lang="en" hreflang="en" data-title="Vector space" data-language-autonym="English" data-language-local-name="anglų" 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/Vektora_spaco" title="Vektora spaco – esperanto" lang="eo" hreflang="eo" data-title="Vektora spaco" 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/Espacio_vectorial" title="Espacio vectorial – ispanų" lang="es" hreflang="es" data-title="Espacio vectorial" data-language-autonym="Español" data-language-local-name="ispanų" 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/Vektorruum" title="Vektorruum – estų" lang="et" hreflang="et" data-title="Vektorruum" data-language-autonym="Eesti" data-language-local-name="estų" 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/Bektore_espazio" title="Bektore espazio – baskų" lang="eu" hreflang="eu" data-title="Bektore espazio" data-language-autonym="Euskara" data-language-local-name="baskų" 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%81%D8%B6%D8%A7%DB%8C_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1%DB%8C" title="فضای برداری – persų" lang="fa" hreflang="fa" data-title="فضای برداری" data-language-autonym="فارسی" data-language-local-name="persų" 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/Vektoriavaruus" title="Vektoriavaruus – suomių" lang="fi" hreflang="fi" data-title="Vektoriavaruus" data-language-autonym="Suomi" data-language-local-name="suomių" 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/Espace_vectoriel" title="Espace vectoriel – prancūzų" lang="fr" hreflang="fr" data-title="Espace vectoriel" data-language-autonym="Français" data-language-local-name="prancūzų" 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/Sp%C3%A1s_veicteoireach" title="Spás veicteoireach – airių" lang="ga" hreflang="ga" data-title="Spás veicteoireach" data-language-autonym="Gaeilge" data-language-local-name="airių" 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/Espazo_vectorial" title="Espazo vectorial – galisų" lang="gl" hreflang="gl" data-title="Espazo vectorial" data-language-autonym="Galego" data-language-local-name="galisų" 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%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי – hebrajų" lang="he" hreflang="he" data-title="מרחב וקטורי" data-language-autonym="עברית" data-language-local-name="hebrajų" 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%B8%E0%A4%A6%E0%A4%BF%E0%A4%B6_%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="सदिश बीजगणित – hindi" lang="hi" hreflang="hi" data-title="सदिश बीजगणित" data-language-autonym="हिन्दी" data-language-local-name="hindi" 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/Vektorski_prostor" title="Vektorski prostor – kroatų" lang="hr" hreflang="hr" data-title="Vektorski prostor" data-language-autonym="Hrvatski" data-language-local-name="kroatų" 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/Vektort%C3%A9r" title="Vektortér – vengrų" lang="hu" hreflang="hu" data-title="Vektortér" data-language-autonym="Magyar" data-language-local-name="vengrų" 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%8E%D5%A5%D5%AF%D5%BF%D5%B8%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%BF%D5%A1%D6%80%D5%A1%D5%AE%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Վեկտորական տարածություն – armėnų" lang="hy" hreflang="hy" data-title="Վեկտորական տարածություն" data-language-autonym="Հայերեն" data-language-local-name="armėnų" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Spatio_vectorial" title="Spatio vectorial – tarpinė" lang="ia" hreflang="ia" data-title="Spatio vectorial" data-language-autonym="Interlingua" data-language-local-name="tarpinė" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ruang_vektor" title="Ruang vektor – indoneziečių" lang="id" hreflang="id" data-title="Ruang vektor" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziečių" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Vigurr%C3%BAm" title="Vigurrúm – islandų" lang="is" hreflang="is" data-title="Vigurrúm" data-language-autonym="Íslenska" data-language-local-name="islandų" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spazio_vettoriale" title="Spazio vettoriale – italų" lang="it" hreflang="it" data-title="Spazio vettoriale" data-language-autonym="Italiano" data-language-local-name="italų" 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%99%E3%82%AF%E3%83%88%E3%83%AB%E7%A9%BA%E9%96%93" title="ベクトル空間 – japonų" lang="ja" hreflang="ja" data-title="ベクトル空間" data-language-autonym="日本語" data-language-local-name="japonų" 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/%EB%B2%A1%ED%84%B0_%EA%B3%B5%EA%B0%84" title="벡터 공간 – korėjiečių" lang="ko" hreflang="ko" data-title="벡터 공간" data-language-autonym="한국어" data-language-local-name="korėjiečių" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B4%D1%83%D0%BA_%D0%BC%D0%B5%D0%B9%D0%BA%D0%B8%D0%BD%D0%B4%D0%B8%D0%BA" title="Вектордук мейкиндик – kirgizų" lang="ky" hreflang="ky" data-title="Вектордук мейкиндик" data-language-autonym="Кыргызча" data-language-local-name="kirgizų" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Spatium_vectoriale" title="Spatium vectoriale – lotynų" lang="la" hreflang="la" data-title="Spatium vectoriale" data-language-autonym="Latina" data-language-local-name="lotynų" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Spazzi_vettorial" title="Spazzi vettorial – lombardų" lang="lmo" hreflang="lmo" data-title="Spazzi vettorial" data-language-autonym="Lombard" data-language-local-name="lombardų" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BB%80%E0%BA%A7%E0%BA%B1%E0%BA%81%E0%BB%80%E0%BA%95%E0%BA%B5" title="ເວັກເຕີ – laosiečių" lang="lo" hreflang="lo" data-title="ເວັກເຕີ" data-language-autonym="ລາວ" data-language-local-name="laosiečių" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Vektoru_telpa" title="Vektoru telpa – latvių" lang="lv" hreflang="lv" data-title="Vektoru telpa" data-language-autonym="Latviešu" data-language-local-name="latvių" 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%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D1%81%D0%BA%D0%B8_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Векторски простор – makedonų" lang="mk" hreflang="mk" data-title="Векторски простор" data-language-autonym="Македонски" data-language-local-name="makedonų" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%A6%E0%B4%BF%E0%B4%B6%E0%B4%B8%E0%B4%AE%E0%B4%B7%E0%B5%8D%E0%B4%9F%E0%B4%BF" title="സദിശസമഷ്ടി – malajalių" lang="ml" hreflang="ml" data-title="സദിശസമഷ്ടി" data-language-autonym="മലയാളം" data-language-local-name="malajalių" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ruang_vektor" title="Ruang vektor – malajiečių" lang="ms" hreflang="ms" data-title="Ruang vektor" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiečių" 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/Vectorruimte" title="Vectorruimte – olandų" lang="nl" hreflang="nl" data-title="Vectorruimte" data-language-autonym="Nederlands" data-language-local-name="olandų" 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/Vektorrom" title="Vektorrom – naujoji norvegų" lang="nn" hreflang="nn" data-title="Vektorrom" data-language-autonym="Norsk nynorsk" data-language-local-name="naujoji norvegų" 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/Vektorrom" title="Vektorrom – norvegų bukmolas" lang="nb" hreflang="nb" data-title="Vektorrom" data-language-autonym="Norsk bokmål" data-language-local-name="norvegų bukmolas" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Espaci_vectoriau" title="Espaci vectoriau – očitarų" lang="oc" hreflang="oc" data-title="Espaci vectoriau" data-language-autonym="Occitan" data-language-local-name="očitarų" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%88%E0%A8%95%E0%A8%9F%E0%A8%B0_%E0%A8%B8%E0%A8%AA%E0%A9%87%E0%A8%B8" title="ਵੈਕਟਰ ਸਪੇਸ – pendžabų" lang="pa" hreflang="pa" data-title="ਵੈਕਟਰ ਸਪੇਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pendžabų" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przestrze%C5%84_liniowa" title="Przestrzeń liniowa – lenkų" lang="pl" hreflang="pl" data-title="Przestrzeń liniowa" data-language-autonym="Polski" data-language-local-name="lenkų" 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/Spassi_vetorial" title="Spassi vetorial – italų kalbos Pjemonto tarmė" lang="pms" hreflang="pms" data-title="Spassi vetorial" data-language-autonym="Piemontèis" data-language-local-name="italų kalbos Pjemonto tarmė" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%DB%8C%DA%A9%D9%B9%D8%B1_%D8%B3%D9%BE%DB%8C%D8%B3" title="ویکٹر سپیس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ویکٹر سپیس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Espa%C3%A7o_vetorial" title="Espaço vetorial – portugalų" lang="pt" hreflang="pt" data-title="Espaço vetorial" data-language-autonym="Português" data-language-local-name="portugalų" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro badge-Q17437798 badge-goodarticle mw-list-item" title="vertingas straipsnis"><a href="https://ro.wikipedia.org/wiki/Spa%C8%9Biu_vectorial" title="Spațiu vectorial – rumunų" lang="ro" hreflang="ro" data-title="Spațiu vectorial" data-language-autonym="Română" data-language-local-name="rumunų" 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%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Векторное пространство – rusų" lang="ru" hreflang="ru" data-title="Векторное пространство" data-language-autonym="Русский" data-language-local-name="rusų" 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/Spazziu_vitturiali" title="Spazziu vitturiali – siciliečių" lang="scn" hreflang="scn" data-title="Spazziu vitturiali" data-language-autonym="Sicilianu" data-language-local-name="siciliečių" 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/Vektorski_prostor" title="Vektorski prostor – serbų-kroatų" lang="sh" hreflang="sh" data-title="Vektorski prostor" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbų-kroatų" 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/Vector_space" title="Vector space – Simple English" lang="en-simple" hreflang="en-simple" data-title="Vector space" 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/Vektorov%C3%BD_priestor" title="Vektorový priestor – slovakų" lang="sk" hreflang="sk" data-title="Vektorový priestor" data-language-autonym="Slovenčina" data-language-local-name="slovakų" 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/Vektorski_prostor" title="Vektorski prostor – slovėnų" lang="sl" hreflang="sl" data-title="Vektorski prostor" data-language-autonym="Slovenščina" data-language-local-name="slovėnų" 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/Hap%C3%ABsira_vektoriale" title="Hapësira vektoriale – albanų" lang="sq" hreflang="sq" data-title="Hapësira vektoriale" data-language-autonym="Shqip" data-language-local-name="albanų" 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%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D1%81%D0%BA%D0%B8_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Векторски простор – serbų" lang="sr" hreflang="sr" data-title="Векторски простор" data-language-autonym="Српски / srpski" data-language-local-name="serbų" 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/Linj%C3%A4rt_rum" title="Linjärt rum – švedų" lang="sv" hreflang="sv" data-title="Linjärt rum" data-language-autonym="Svenska" data-language-local-name="švedų" 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%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%AF%E0%AE%A9%E0%AF%8D_%E0%AE%B5%E0%AF%86%E0%AE%B3%E0%AE%BF" title="திசையன் வெளி – tamilų" lang="ta" hreflang="ta" data-title="திசையன் வெளி" data-language-autonym="தமிழ்" data-language-local-name="tamilų" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Espasyong_bektor" title="Espasyong bektor – tagalogų" lang="tl" hreflang="tl" data-title="Espasyong bektor" data-language-autonym="Tagalog" data-language-local-name="tagalogų" 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/Vekt%C3%B6r_uzay%C4%B1" title="Vektör uzayı – turkų" lang="tr" hreflang="tr" data-title="Vektör uzayı" data-language-autonym="Türkçe" data-language-local-name="turkų" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BD%D0%B8%D0%B9_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%96%D1%80" title="Векторний простір – ukrainiečių" lang="uk" hreflang="uk" data-title="Векторний простір" data-language-autonym="Українська" data-language-local-name="ukrainiečių" 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/%D8%B3%D9%85%D8%AA%DB%8C%DB%81_%D9%85%DA%A9%D8%A7%DA%BA" title="سمتیہ مکاں – urdų" lang="ur" hreflang="ur" data-title="سمتیہ مکاں" data-language-autonym="اردو" data-language-local-name="urdų" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Spasio_vetorial" title="Spasio vetorial – venetų" lang="vec" hreflang="vec" data-title="Spasio vetorial" data-language-autonym="Vèneto" data-language-local-name="venetų" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kh%C3%B4ng_gian_vect%C6%A1" title="Không gian vectơ – vietnamiečių" lang="vi" hreflang="vi" data-title="Không gian vectơ" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamiečių" 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/%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4" title="向量空间 – kinų kalbos vu tarmė" lang="wuu" hreflang="wuu" data-title="向量空间" data-language-autonym="吴语" data-language-local-name="kinų kalbos vu tarmė" 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/%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4" title="向量空间 – kinų" lang="zh" hreflang="zh" data-title="向量空间" data-language-autonym="中文" data-language-local-name="kinų" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%9F%A2%E9%87%8F%E7%A9%BA%E9%96%93" title="矢量空間 – klasikinė kinų" lang="lzh" hreflang="lzh" data-title="矢量空間" data-language-autonym="文言" data-language-local-name="klasikinė kinų" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Hi%C3%B2ng-li%C5%8Dng_khong-kan" title="Hiòng-liōng khong-kan – kinų kalbos pietų minų tarmė" lang="nan" hreflang="nan" data-title="Hiòng-liōng khong-kan" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="kinų kalbos pietų minų tarmė" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%90%91%E9%87%8F%E7%A9%BA%E9%96%93" title="向量空間 – kinų kalbos Kantono tarmė" lang="yue" hreflang="yue" data-title="向量空間" data-language-autonym="粵語" data-language-local-name="kinų kalbos Kantono tarmė" 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/Q125977#sitelinks-wikipedia" title="Keisti tarpkalbines nuorodas" class="wbc-editpage">Keisti nuorodas</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="Vardų sritys"> <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/Vektorin%C4%97_erdv%C4%97" title="Rodyti puslapio turinį [c]" accesskey="c"><span>Straipsnis</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Aptarimas:Vektorin%C4%97_erdv%C4%97" rel="discussion" title="Puslapio turinio aptarimas [t]" accesskey="t"><span>Aptarimas</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="Change language variant" > <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">lietuvių</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="Žiūrėti"> <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/Vektorin%C4%97_erdv%C4%97"><span>Skaityti</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&veaction=edit" title="Redaguoti šį puslapį [v]" accesskey="v"><span>Keisti</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=edit" title="Redaguoti šio puslapio išeities kodą [e]" accesskey="e"><span>Keisti vikitekstą</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=history" title="Ankstesnės puslapio versijos [h]" accesskey="h"><span>Istorija</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <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="Įrankiai" > <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">Įrankiai</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">Įrankiai</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">paslėpti</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Daugiau nustatymų" > <div class="vector-menu-heading"> Veiksmai </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/Vektorin%C4%97_erdv%C4%97"><span>Skaityti</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&veaction=edit" title="Redaguoti šį puslapį [v]" accesskey="v"><span>Keisti</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=edit" title="Redaguoti šio puslapio išeities kodą [e]" accesskey="e"><span>Keisti vikitekstą</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=history"><span>Istorija</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Bendra </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Specialus:Kas_%C4%AF_%C4%8Dia_rodo/Vektorin%C4%97_erdv%C4%97" title="Viki puslapių sąrašas, kuris nurodo čia [j]" accesskey="j"><span>Susiję straipsniai</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Specialus:Pakeitimai_susijusiuose_puslapiuose/Vektorin%C4%97_erdv%C4%97" rel="nofollow" title="Paskutiniai keitimai puslapiuose, pasiekiamuose iš šio puslapio [k]" accesskey="k"><span>Susiję keitimai</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Specialus:Specialieji_puslapiai" title="Specialiųjų puslapių sąrašas [q]" accesskey="q"><span>Specialieji puslapiai</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&oldid=7178995" title="Nuolatinė nuoroda į šią puslapio versiją"><span>Nuolatinė nuoroda</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=info" title="Daugiau žinių apie šį puslapį"><span>Puslapio informacija</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Specialus:CiteThisPage&page=Vektorin%C4%97_erdv%C4%97&id=7178995&wpFormIdentifier=titleform" title="Informacija kaip cituoti šį puslapį"><span>Cituoti straipsnį</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Specialus:UrlShortener&url=https%3A%2F%2Flt.wikipedia.org%2Fwiki%2FVektorin%25C4%2597_erdv%25C4%2597"><span>Gauti sutrumpintą URL nuorodą</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Specialus:QrCode&url=https%3A%2F%2Flt.wikipedia.org%2Fwiki%2FVektorin%25C4%2597_erdv%25C4%2597"><span>Atsisiųsti QR kodą</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"> Spausdinti/eksportuoti </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=Specialus:Book&bookcmd=book_creator&referer=Vektorin%C4%97+erdv%C4%97"><span>Kurti knygą</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Specialus:DownloadAsPdf&page=Vektorin%C4%97_erdv%C4%97&action=show-download-screen"><span>Parsisiųsti kaip PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&printable=yes" title="Šio puslapio versija spausdinimui [p]" accesskey="p"><span>Versija spausdinimui</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"> Kituose projektuose </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:Vector_spaces" hreflang="en"><span>Vikiteka</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/Q125977" title="Nuoroda į susietą duomenų saugyklos įrašą [g]" accesskey="g"><span>Vikiduomenys įrašas</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Išvaizda"> <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">Išvaizda</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">paslėpti</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">Straipsnis iš Vikipedijos, laisvosios enciklopedijos.</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="lt" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Vaizdas:Vector_space_illust.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Vector_space_illust.svg/220px-Vector_space_illust.svg.png" decoding="async" width="220" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Vector_space_illust.svg/330px-Vector_space_illust.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Vector_space_illust.svg/440px-Vector_space_illust.svg.png 2x" data-file-width="454" data-file-height="555" /></a><figcaption>Vektorinė erdvė yra rinkinys objektų, vadinamų <a href="/wiki/Vektorius" title="Vektorius">vektoriais</a>, kurie gali būti sudedami arba galimas jų <a href="/wiki/Mastelis" title="Mastelis">mastelio</a> keitimas</figcaption></figure> <p><b>Vektorinė erdvė</b> arba <b>tiesinė erdvė</b> – <a href="/wiki/Vektorius" title="Vektorius">vektorių</a> <a href="/wiki/Aib%C4%97" title="Aibė">aibė</a> su joje apibrėžtomis <a href="/wiki/Sud%C4%97tis" title="Sudėtis">sudėties</a> ir <a href="/wiki/Daugyba" title="Daugyba">daugybos</a> iš <a href="/wiki/Skaliaras" class="mw-disambig" title="Skaliaras">skaliarinio dydžio</a> operacijomis, tenkinančiomis tam tikras, žemiau išvardintas aksiomas. Vektorinės erdvės yra pagrindiniai tiesinės algebros studijų objektai, naudojami <a href="/wiki/Matematika" title="Matematika">matematikoje</a>, moksle ir inžinerijoje. </p><p>Pačios paprasčiausios vektorinės erdvės yra dvimatės arba trimatės <a href="/wiki/Euklidin%C4%97_erdv%C4%97" title="Euklidinė erdvė">Euklido erdvės</a>. Šiose erdvėse vektoriai aprašomi skaičių poromis arba trejetais ir dažnai apibūdinami kaip geometriniai vektoriai, su dydžiu ir kryptimi, vaizduojami kaip strėlės. Šie vektoriai gali būti sudedami naudojant lygiagretainio taisyklę (vektorių sudėtis) arba dauginami iš sveikų skaičių. Šių operacijų metu geometrinių vektorių elgsena pasiūlo vektorių elgsenos modelį daug abstraktesnėse vektorių erdvėse, kurioms nėra būtina turėti geometrinę interpretaciją. Pavyzdžiui, (realūs) polinomai suformuoja vektorinę erdvę. </p><p>Vektorinės erdvės pirminės sąvokos – plokštuma arba trimatė erdvė su koordinačių sistema pirmą kartą apie 1636 m. nagrinėjo <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Renė Dekartas</a> ir <a href="/wiki/Pjeras_Ferma" title="Pjeras Ferma">Pjeras Ferma</a>, o vektorinės erdvės dabartinę sampratą 1888 m. pradėjo vartoti italų matematikas <a href="/w/index.php?title=Giuseppe_Peano&action=edit&redlink=1" class="new" title="Giuseppe Peano (puslapis neegzistuoja)">Džuzepė Peanas</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Formalus_apibrėžimas"><span id="Formalus_apibr.C4.97.C5.BEimas"></span>Formalus apibrėžimas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&veaction=edit&section=1" title="Redaguoti skyrelį: Formalus apibrėžimas" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=edit&section=1" title="Edit section's source code: Formalus apibrėžimas"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tarkime, kad <i>F</i> yra <a href="/wiki/Laukas_(matematika)" class="mw-redirect" title="Laukas (matematika)">laukas</a> (pavyzdžiui, realieji arba kompleksiniai skaičiai), kurio elementai yra skaliarai. </p><p>Vektorinė erdvė virš lauko <i>F</i> yra toliau pateiktas aksiomas tenkinanti aibė <i>V</i> kartu su apibrėžtomis binarinėmis operacijomis: </p> <ul><li><i>Vektorių sudėtis</i>: <i>V</i> × <i>V</i> → <i>V</i>, žymima <b>v</b> + <b>w</b>, kur <b>v</b>, <b>w</b> ∈ <i>V</i>.</li> <li><i>Daugyba iš skaliaro</i>: <i>F</i> × <i>V</i> → <i>V</i>, žymima <i>a</i><b>v</b>, kur <i>a</i> ∈ <i>F</i> and <b>v</b> ∈ <i>V</i>.</li></ul> <p>Tiesinėje erdvėje galioja šios aksiomos: </p> <ol><li>Vektorių sudėtis yra <a href="/wiki/Asociatyvumas" title="Asociatyvumas">asociatyvi</a>: <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 \forall \mathbf {u} ,\mathbf {v} ,\mathbf {w} \in V:\mathbf {u} +(\mathbf {v} +\mathbf {w} )=(\mathbf {u} +\mathbf {v} )+\mathbf {w} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \mathbf {u} ,\mathbf {v} ,\mathbf {w} \in V:\mathbf {u} +(\mathbf {v} +\mathbf {w} )=(\mathbf {u} +\mathbf {v} )+\mathbf {w} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec12afe27775cdac3fc8955f7e223f57bbfb76c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.133ex; height:2.843ex;" alt="{\displaystyle \forall \mathbf {u} ,\mathbf {v} ,\mathbf {w} \in V:\mathbf {u} +(\mathbf {v} +\mathbf {w} )=(\mathbf {u} +\mathbf {v} )+\mathbf {w} .}"></span></dd></dl></li> <li>Vektorių sudėtis yra <a href="/wiki/Komutatyvumas" title="Komutatyvumas">komutatyvi</a>: <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 \forall \mathbf {v} ,\mathbf {w} \in V:\mathbf {v} +\mathbf {w} =\mathbf {w} +\mathbf {v} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \mathbf {v} ,\mathbf {w} \in V:\mathbf {v} +\mathbf {w} =\mathbf {w} +\mathbf {v} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/282d4bdfbc321975804630b5e3f536518b272c9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:28.344ex; height:2.509ex;" alt="{\displaystyle \forall \mathbf {v} ,\mathbf {w} \in V:\mathbf {v} +\mathbf {w} =\mathbf {w} +\mathbf {v} .}"></span></dd></dl></li> <li>Vektorių sudėčiai egzistuoja vienetinis elementas: <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 \exists \mathbf {0} \in V:\mathbf {v} +\mathbf {0} =\mathbf {v} ,\forall \mathbf {v} \in V.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists \mathbf {0} \in V:\mathbf {v} +\mathbf {0} =\mathbf {v} ,\forall \mathbf {v} \in V.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ef289582f9a2e8352a0c874a5d5eda8bf86d706" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:28.304ex; height:2.509ex;" alt="{\displaystyle \exists \mathbf {0} \in V:\mathbf {v} +\mathbf {0} =\mathbf {v} ,\forall \mathbf {v} \in V.}"></span></dd></dl></li> <li>Vektorių sudėtis turi priešingąjį elementą: <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 \forall \mathbf {v} \in V,\exists \mathbf {w} \in V:\mathbf {v} +\mathbf {w} =0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>,</mo> <mi mathvariant="normal">∃</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \mathbf {v} \in V,\exists \mathbf {w} \in V:\mathbf {v} +\mathbf {w} =0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5178e925d0611b13924cebd142959ad6dc03db3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:29.244ex; height:2.509ex;" alt="{\displaystyle \forall \mathbf {v} \in V,\exists \mathbf {w} \in V:\mathbf {v} +\mathbf {w} =0.}"></span></dd></dl></li> <li>Vektorių sumos daugyba iš skaliaro yra <a href="/w/index.php?title=Distributyvumas&action=edit&redlink=1" class="new" title="Distributyvumas (puslapis neegzistuoja)">distributyvi</a>: <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 \forall a\in F,\forall \mathbf {v} ,\mathbf {w} \in V:a(\mathbf {v} +\mathbf {w} )=a\mathbf {v} +a\mathbf {w} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">w</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in F,\forall \mathbf {v} ,\mathbf {w} \in V:a(\mathbf {v} +\mathbf {w} )=a\mathbf {v} +a\mathbf {w} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db03ecefb99f62348cb6129f91d6fff4a1f49bef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.981ex; height:2.843ex;" alt="{\displaystyle \forall a\in F,\forall \mathbf {v} ,\mathbf {w} \in V:a(\mathbf {v} +\mathbf {w} )=a\mathbf {v} +a\mathbf {w} .}"></span></dd></dl></li> <li>Vektoriaus daugyba iš skaliarų sumos yra distributyvi: <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 \forall a,b\in F,\forall \mathbf {v} \in V:(a+b)\mathbf {v} =a\mathbf {v} +b\mathbf {v} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b\in F,\forall \mathbf {v} \in V:(a+b)\mathbf {v} =a\mathbf {v} +b\mathbf {v} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c9d9e80c358158d299343e475594e22bd2034d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.361ex; height:2.843ex;" alt="{\displaystyle \forall a,b\in F,\forall \mathbf {v} \in V:(a+b)\mathbf {v} =a\mathbf {v} +b\mathbf {v} .}"></span></dd></dl></li> <li>Daugyba iš skaliaro yra suderinama su skaliarų daugyba: <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 \forall a,b\in F,\forall \mathbf {v} \in V:a(b\mathbf {v} )=(ab)\mathbf {v} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>b</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b\in F,\forall \mathbf {v} \in V:a(b\mathbf {v} )=(ab)\mathbf {v} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b6a3611f8d9fec00b7272ed73894ef2876ebe3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.078ex; height:2.843ex;" alt="{\displaystyle \forall a,b\in F,\forall \mathbf {v} \in V:a(b\mathbf {v} )=(ab)\mathbf {v} .}"></span></dd></dl></li> <li>Daugybai iš skaliaro egzistuoja vienetinis elementas: <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 \exists 1\in F:1\mathbf {v} =\mathbf {v} ,\forall \mathbf {v} \in V.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mn>1</mn> <mo>∈</mo> <mi>F</mi> <mo>:</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists 1\in F:1\mathbf {v} =\mathbf {v} ,\forall \mathbf {v} \in V.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06d871d802053136c621d063adb15d1f62767b93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.069ex; height:2.509ex;" alt="{\displaystyle \exists 1\in F:1\mathbf {v} =\mathbf {v} ,\forall \mathbf {v} \in V.}"></span></dd></dl></li></ol> <p>Galima pažymėti, kad septintoji aksioma neteigia asociatyvumo, nes daugyba iš skaliaro (<i>b</i> <b>v</b>) ir skaliarų daugyba (<i>ab</i>) yra skirtingos operacijos. </p><p>Kai kurie šaltiniai įtraukia dar dvi aksiomas: </p> <ol><li><i>V</i> yra uždara vektorių sudėčiai: <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 {u} ,\mathbf {v} \in V\Rightarrow \mathbf {u} +\mathbf {v} \in V.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo stretchy="false">⇒</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {u} ,\mathbf {v} \in V\Rightarrow \mathbf {u} +\mathbf {v} \in V.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/089ca09e06f3a98b253d1872f1a0d4d1141be24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.184ex; height:2.509ex;" alt="{\displaystyle \mathbf {u} ,\mathbf {v} \in V\Rightarrow \mathbf {u} +\mathbf {v} \in V.}"></span></dd></dl></li> <li><i>V</i> yra uždara skaliarų daugybai: <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 a\in F,\mathbf {v} \in V\Rightarrow a\mathbf {v} \in V.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo stretchy="false">⇒</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\in F,\mathbf {v} \in V\Rightarrow a\mathbf {v} \in V.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08ba23366b56853bf16ec50d1dd47e09bfdd7dc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.414ex; height:2.509ex;" alt="{\displaystyle a\in F,\mathbf {v} \in V\Rightarrow a\mathbf {v} \in V.}"></span></dd></dl></li></ol> <p>Tačiau paprastai laikoma, kad šios aksiomos yra numanomos iš operacijų apibrėžimų. </p> <div class="mw-heading mw-heading2"><h2 id="Elementarios_savybės"><span id="Elementarios_savyb.C4.97s"></span>Elementarios savybės</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&veaction=edit&section=2" title="Redaguoti skyrelį: Elementarios savybės" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=edit&section=2" title="Edit section's source code: Elementarios savybės"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Yra keletas savybių, kurios įrodomos naudojant minėtas aksiomas: </p> <ul><li>Nulinis vektorius <b>0</b> ∈ <i>V</i> yra unikalus: <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 \exists \mathbf {0_{1}} ,\mathbf {0_{2}} \in V,\forall \mathbf {v} \in V:\mathbf {0_{1}} +\mathbf {v} =\mathbf {v} ,\mathbf {0_{2}} +\mathbf {v} =\mathbf {v} \Rightarrow \mathbf {0_{1}} =\mathbf {0_{2}} =\mathbf {0} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mn mathvariant="bold">0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mn mathvariant="bold">0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>∈</mo> <mi>V</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mn mathvariant="bold">0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mn mathvariant="bold">0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">⇒</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mn mathvariant="bold">0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mn mathvariant="bold">0</mn> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists \mathbf {0_{1}} ,\mathbf {0_{2}} \in V,\forall \mathbf {v} \in V:\mathbf {0_{1}} +\mathbf {v} =\mathbf {v} ,\mathbf {0_{2}} +\mathbf {v} =\mathbf {v} \Rightarrow \mathbf {0_{1}} =\mathbf {0_{2}} =\mathbf {0} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96e4ec134f09c4aac8f42efb676167e7cf4bcdc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:62.691ex; height:2.509ex;" alt="{\displaystyle \exists \mathbf {0_{1}} ,\mathbf {0_{2}} \in V,\forall \mathbf {v} \in V:\mathbf {0_{1}} +\mathbf {v} =\mathbf {v} ,\mathbf {0_{2}} +\mathbf {v} =\mathbf {v} \Rightarrow \mathbf {0_{1}} =\mathbf {0_{2}} =\mathbf {0} .}"></span></dd></dl></li> <li>Nulinio vektoriaus daugybos iš bet kokio skaliaro rezultatas yra nulinis vektorius: <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 \forall a\in F:a\mathbf {0} =\mathbf {0} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>F</mi> <mo>:</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in F:a\mathbf {0} =\mathbf {0} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d8adf309bbb5a27b151cfb9edaba6618ae9e63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.689ex; height:2.176ex;" alt="{\displaystyle \forall a\in F:a\mathbf {0} =\mathbf {0} .}"></span></dd></dl></li> <li>Bet kokio vektoriaus daugybos iš nulio rezultatas yra nulinis vektorius: <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 \forall \mathbf {v} \in V:0\mathbf {v} =\mathbf {0} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \mathbf {v} \in V:0\mathbf {v} =\mathbf {0} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8623d72d378a67e916386f63a6a62f4d9f2d8b2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.924ex; height:2.176ex;" alt="{\displaystyle \forall \mathbf {v} \in V:0\mathbf {v} =\mathbf {0} .}"></span></dd></dl></li> <li>Nenulinio vektoriaus daugybos iš nenulinio skaliaro rezultatas negali būti nulinis vektorius: <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 \forall \mathbf {v} \in V,\forall a\in F:a\mathbf {v} =\mathbf {0} \Leftrightarrow a=0\lor \mathbf {v} =\mathbf {0} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>F</mi> <mo>:</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo stretchy="false">⇔</mo> <mi>a</mi> <mo>=</mo> <mn>0</mn> <mo>∨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \mathbf {v} \in V,\forall a\in F:a\mathbf {v} =\mathbf {0} \Leftrightarrow a=0\lor \mathbf {v} =\mathbf {0} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd7605dbad221624dd6be672e0686455ff84329c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:42.662ex; height:2.509ex;" alt="{\displaystyle \forall \mathbf {v} \in V,\forall a\in F:a\mathbf {v} =\mathbf {0} \Leftrightarrow a=0\lor \mathbf {v} =\mathbf {0} .}"></span></dd></dl></li> <li>Vektorius, priešingas duotajam (−<b>v</b>) yra unikalus: <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 \exists \mathbf {v} ,\mathbf {w_{1}} ,\mathbf {w_{2}} \in V:\mathbf {v} +\mathbf {w_{1}} =\mathbf {0} ,\mathbf {v} +\mathbf {w_{2}} =\mathbf {0} \Rightarrow \mathbf {w_{1}} =\mathbf {w_{2}} =-\mathbf {v} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> <mo stretchy="false">⇒</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists \mathbf {v} ,\mathbf {w_{1}} ,\mathbf {w_{2}} \in V:\mathbf {v} +\mathbf {w_{1}} =\mathbf {0} ,\mathbf {v} +\mathbf {w_{2}} =\mathbf {0} \Rightarrow \mathbf {w_{1}} =\mathbf {w_{2}} =-\mathbf {v} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85a628988831572b7a322dc662d18b89fbb337db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:62.072ex; height:2.509ex;" alt="{\displaystyle \exists \mathbf {v} ,\mathbf {w_{1}} ,\mathbf {w_{2}} \in V:\mathbf {v} +\mathbf {w_{1}} =\mathbf {0} ,\mathbf {v} +\mathbf {w_{2}} =\mathbf {0} \Rightarrow \mathbf {w_{1}} =\mathbf {w_{2}} =-\mathbf {v} .}"></span></dd></dl></li> <li>Vektoriaus daugybos iš neigiamo vienetinio skaliaro rezultatas yra vektorius, priešingas pradiniam: <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 \forall \mathbf {v} \in V:(-1)\mathbf {v} =-\mathbf {v} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \mathbf {v} \in V:(-1)\mathbf {v} =-\mathbf {v} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4995a12fd4c401f19e41b28b412af3d2edec1f42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.424ex; height:2.843ex;" alt="{\displaystyle \forall \mathbf {v} \in V:(-1)\mathbf {v} =-\mathbf {v} .}"></span></dd></dl></li> <li>Minuso ženklas daugyboje iš skaliaro gali būti perkeliamas laisvai: <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 \forall a\in F,\forall \mathbf {v} \in V:a(-\mathbf {v} )=(-a)\mathbf {v} =-(a\mathbf {v} ).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>∈</mo> <mi>V</mi> <mo>:</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in F,\forall \mathbf {v} \in V:a(-\mathbf {v} )=(-a)\mathbf {v} =-(a\mathbf {v} ).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb5ee4faa6709cb188c1a7ecda4a44e1caa2fba3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.025ex; height:2.843ex;" alt="{\displaystyle \forall a\in F,\forall \mathbf {v} \in V:a(-\mathbf {v} )=(-a)\mathbf {v} =-(a\mathbf {v} ).}"></span></dd></dl></li></ul> <div class="mw-heading mw-heading2"><h2 id="Šaltiniai"><span id=".C5.A0altiniai"></span>Šaltiniai</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&veaction=edit&section=3" title="Redaguoti skyrelį: Šaltiniai" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vektorin%C4%97_erdv%C4%97&action=edit&section=3" title="Edit section's source code: Šaltiniai"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.vle.lt/straipsnis/vektorine-erdve/">vektorinė erdvė</a>(parengė Petras Vaškas). <a href="/wiki/Visuotin%C4%97_lietuvi%C5%B3_enciklopedija" title="Visuotinė lietuvių enciklopedija">Visuotinė lietuvių enciklopedija</a> (tikrinta 2024-02-03).</span> </li> </ol> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Rodomas puslapis "<a dir="ltr" href="https://lt.wikipedia.org/w/index.php?title=Vektorinė_erdvė&oldid=7178995">https://lt.wikipedia.org/w/index.php?title=Vektorinė_erdvė&oldid=7178995</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Specialus:Kategorijos" title="Specialus:Kategorijos">Kategorija</a>: <ul><li><a href="/wiki/Kategorija:Vektoriai" title="Kategorija:Vektoriai">Vektoriai</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Šis puslapis paskutinį kartą keistas 3 vasario 2024 16:30.</li> <li id="footer-info-copyright">Tekstas pateikiamas pagal <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution/Share-Alike Licenciją</a>; gali būti taikomos papildomos sąlygos. Detaliau – <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">Terms of Use</a> .</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privatumo politika</a></li> <li id="footer-places-about"><a href="/wiki/Vikipedija:Apie">Apie Vikipediją</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Vikipedija:General_disclaimer">Jokių garantijų</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Kūrėjai</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/lt.wikipedia.org">Statistika</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Slapukų politika</a></li> <li id="footer-places-mobileview"><a href="//lt.m.wikipedia.org/w/index.php?title=Vektorin%C4%97_erdv%C4%97&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobili peržiūra</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-847495b4dd-wkr6d","wgBackendResponseTime":152,"wgPageParseReport":{"limitreport":{"cputime":"0.033","walltime":"0.109","ppvisitednodes":{"value":161,"limit":1000000},"postexpandincludesize":{"value":336,"limit":2097152},"templateargumentsize":{"value":70,"limit":2097152},"expansiondepth":{"value":6,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":1106,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 6.967 1 -total","100.00% 6.967 1 Šablonas:Išnašos"," 42.94% 2.992 1 Šablonas:Vle"]},"cachereport":{"origin":"mw-web.codfw.main-7c54859c9b-kdffc","timestamp":"20241111175300","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Vektorin\u0117 erdv\u0117","url":"https:\/\/lt.wikipedia.org\/wiki\/Vektorin%C4%97_erdv%C4%97","sameAs":"http:\/\/www.wikidata.org\/entity\/Q125977","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q125977","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-12-17T22:16:00Z","dateModified":"2024-02-03T14:30:08Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/c\/c8\/Vector_space_illust.svg"}</script> </body> </html>