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međutim, to nije obavezno" class=""><span>Napravi korisnički račun</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=Posebno:Korisni%C4%8Dka_prijava&returnto=Vektorski+prostor" title="Predlažemo vam da se prijavite, iako to nije obavezno [o]" accesskey="o" class=""><span>Prijavi me</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="Više opcija" > <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="Lični alati" > <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">Lični alati</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Korisnički meni" > <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_bs.wikipedia.org&uselang=bs"><span>Donacije</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebno:Napravi_ra%C4%8Dun&returnto=Vektorski+prostor" title="Predlažemo vam da napravite račun i prijavite se; međutim, to nije obavezno"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Napravi korisnički račun</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebno:Korisni%C4%8Dka_prijava&returnto=Vektorski+prostor" title="Predlažemo vam da se prijavite, iako to nije obavezno [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Prijavi me</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"> Stranice za odjavljene urednike <a href="/wiki/Pomo%C4%87:Uvod" aria-label="Saznajte više o uređivanju"><span>detaljnije</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Posebno:Moji_doprinosi" title="Spisak izmjena napravljenih s ove IP-adrese [y]" accesskey="y"><span>Doprinosi</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Posebno:Moj_razgovor" title="Rasprava o izmjenama s ove IP-adrese [n]" accesskey="n"><span>Razgovor</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\"\u003Ezatvori\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=\"bs\" dir=\"ltr\"\u003E\u003Ctable class=\"fmbox fmbox-system\" role=\"presentation\" style=\"border:1px solid #409262; 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Dostupno na 77 jezika" > <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 jezika</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 – afrikans" lang="af" hreflang="af" data-title="Vektorruimte" data-language-autonym="Afrikaans" data-language-local-name="afrikans" 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 – arapski" lang="ar" hreflang="ar" data-title="فضاء متجهي" data-language-autonym="العربية" data-language-local-name="arapski" 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 – asturijski" lang="ast" hreflang="ast" data-title="Espaciu vectorial" data-language-autonym="Asturianu" data-language-local-name="asturijski" 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 – baškirski" lang="ba" hreflang="ba" data-title="Векторлы арауыҡ" data-language-autonym="Башҡортса" data-language-local-name="baškirski" 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 – bjeloruski" lang="be" hreflang="be" data-title="Вектарная прастора" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" 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 – bugarski" lang="bg" hreflang="bg" data-title="Линейно пространство" data-language-autonym="Български" data-language-local-name="bugarski" 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 – bengalski" lang="bn" hreflang="bn" data-title="সদিক রাশির বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle mw-list-item" title="istaknuti članak"><a href="https://ca.wikipedia.org/wiki/Espai_vectorial" title="Espai vectorial – katalonski" lang="ca" hreflang="ca" data-title="Espai vectorial" data-language-autonym="Català" data-language-local-name="katalonski" 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 – centralnokurdski" lang="ckb" hreflang="ckb" data-title="بۆشاییی ئاڕاستەبڕەکان" data-language-autonym="کوردی" data-language-local-name="centralnokurdski" 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 – češki" lang="cs" hreflang="cs" data-title="Vektorový prostor" data-language-autonym="Čeština" data-language-local-name="češki" 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 – čuvaški" lang="cv" hreflang="cv" data-title="Векторла уçлăх" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" 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 – velški" lang="cy" hreflang="cy" data-title="Gofod fector" data-language-autonym="Cymraeg" data-language-local-name="velški" 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 – danski" lang="da" hreflang="da" data-title="Vektorrum" data-language-autonym="Dansk" data-language-local-name="danski" 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 – njemački" lang="de" hreflang="de" data-title="Vektorraum" data-language-autonym="Deutsch" data-language-local-name="njemački" 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 – grčki" lang="el" hreflang="el" data-title="Διανυσματικός χώρος" data-language-autonym="Ελληνικά" data-language-local-name="grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="dobar članak"><a href="https://en.wikipedia.org/wiki/Vector_space" title="Vector space – engleski" lang="en" hreflang="en" data-title="Vector space" data-language-autonym="English" data-language-local-name="engleski" 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 – španski" lang="es" hreflang="es" data-title="Espacio vectorial" data-language-autonym="Español" data-language-local-name="španski" 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 – estonski" lang="et" hreflang="et" data-title="Vektorruum" data-language-autonym="Eesti" data-language-local-name="estonski" 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 – baskijski" lang="eu" hreflang="eu" data-title="Bektore espazio" data-language-autonym="Euskara" data-language-local-name="baskijski" 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 – perzijski" lang="fa" hreflang="fa" data-title="فضای برداری" data-language-autonym="فارسی" data-language-local-name="perzijski" 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 – finski" lang="fi" hreflang="fi" data-title="Vektoriavaruus" data-language-autonym="Suomi" data-language-local-name="finski" 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 – francuski" lang="fr" hreflang="fr" data-title="Espace vectoriel" data-language-autonym="Français" data-language-local-name="francuski" 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 – irski" lang="ga" hreflang="ga" data-title="Spás veicteoireach" data-language-autonym="Gaeilge" data-language-local-name="irski" 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 – galicijski" lang="gl" hreflang="gl" data-title="Espazo vectorial" data-language-autonym="Galego" data-language-local-name="galicijski" 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 – hebrejski" lang="he" hreflang="he" data-title="מרחב וקטורי" data-language-autonym="עברית" data-language-local-name="hebrejski" 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 – hrvatski" lang="hr" hreflang="hr" data-title="Vektorski prostor" data-language-autonym="Hrvatski" data-language-local-name="hrvatski" 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 – mađarski" lang="hu" hreflang="hu" data-title="Vektortér" data-language-autonym="Magyar" data-language-local-name="mađarski" 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 – armenski" lang="hy" hreflang="hy" data-title="Վեկտորական տարածություն" data-language-autonym="Հայերեն" data-language-local-name="armenski" 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 – interlingva" lang="ia" hreflang="ia" data-title="Spatio vectorial" data-language-autonym="Interlingua" data-language-local-name="interlingva" 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 – indonezijski" lang="id" hreflang="id" data-title="Ruang vektor" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" 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 – islandski" lang="is" hreflang="is" data-title="Vigurrúm" data-language-autonym="Íslenska" data-language-local-name="islandski" 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 – italijanski" lang="it" hreflang="it" data-title="Spazio vettoriale" data-language-autonym="Italiano" data-language-local-name="italijanski" 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 – japanski" lang="ja" hreflang="ja" data-title="ベクトル空間" data-language-autonym="日本語" data-language-local-name="japanski" 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 – korejski" lang="ko" hreflang="ko" data-title="벡터 공간" data-language-autonym="한국어" data-language-local-name="korejski" 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 – kirgiški" lang="ky" hreflang="ky" data-title="Вектордук мейкиндик" data-language-autonym="Кыргызча" data-language-local-name="kirgiški" 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 – latinski" lang="la" hreflang="la" data-title="Spatium vectoriale" data-language-autonym="Latina" data-language-local-name="latinski" 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 – lombardski" lang="lmo" hreflang="lmo" data-title="Spazzi vettorial" data-language-autonym="Lombard" data-language-local-name="lombardski" 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 – laoski" lang="lo" hreflang="lo" data-title="ເວັກເຕີ" data-language-autonym="ລາວ" data-language-local-name="laoski" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vektorin%C4%97_erdv%C4%97" title="Vektorinė erdvė – litvanski" lang="lt" hreflang="lt" data-title="Vektorinė erdvė" data-language-autonym="Lietuvių" data-language-local-name="litvanski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Vektoru_telpa" title="Vektoru telpa – latvijski" lang="lv" hreflang="lv" data-title="Vektoru telpa" data-language-autonym="Latviešu" data-language-local-name="latvijski" 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 – makedonski" lang="mk" hreflang="mk" data-title="Векторски простор" data-language-autonym="Македонски" data-language-local-name="makedonski" 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 – malajalam" lang="ml" hreflang="ml" data-title="സദിശസമഷ്ടി" data-language-autonym="മലയാളം" data-language-local-name="malajalam" 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 – malajski" lang="ms" hreflang="ms" data-title="Ruang vektor" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" 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 – nizozemski" lang="nl" hreflang="nl" data-title="Vectorruimte" data-language-autonym="Nederlands" data-language-local-name="nizozemski" 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 – norveški (Nynorsk)" lang="nn" hreflang="nn" data-title="Vektorrom" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški (Nynorsk)" 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 – norveški (Bokmal)" lang="nb" hreflang="nb" data-title="Vektorrom" data-language-autonym="Norsk bokmål" data-language-local-name="norveški (Bokmal)" 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 – oksitanski" lang="oc" hreflang="oc" data-title="Espaci vectoriau" data-language-autonym="Occitan" data-language-local-name="oksitanski" 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 – pandžapski" lang="pa" hreflang="pa" data-title="ਵੈਕਟਰ ਸਪੇਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžapski" 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 – poljski" lang="pl" hreflang="pl" data-title="Przestrzeń liniowa" data-language-autonym="Polski" data-language-local-name="poljski" 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 – Piedmontese" lang="pms" hreflang="pms" data-title="Spassi vetorial" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" 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 – portugalski" lang="pt" hreflang="pt" data-title="Espaço vetorial" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro badge-Q17437798 badge-goodarticle mw-list-item" title="dobar članak"><a href="https://ro.wikipedia.org/wiki/Spa%C8%9Biu_vectorial" title="Spațiu vectorial – rumunski" lang="ro" hreflang="ro" data-title="Spațiu vectorial" data-language-autonym="Română" data-language-local-name="rumunski" 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 – ruski" lang="ru" hreflang="ru" data-title="Векторное пространство" data-language-autonym="Русский" data-language-local-name="ruski" 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 – sicilijanski" lang="scn" hreflang="scn" data-title="Spazziu vitturiali" data-language-autonym="Sicilianu" data-language-local-name="sicilijanski" 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 – srpskohrvatski" lang="sh" hreflang="sh" data-title="Vektorski prostor" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpskohrvatski" 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 – slovački" lang="sk" hreflang="sk" data-title="Vektorový priestor" data-language-autonym="Slovenčina" data-language-local-name="slovački" 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 – slovenski" lang="sl" hreflang="sl" data-title="Vektorski prostor" data-language-autonym="Slovenščina" data-language-local-name="slovenski" 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 – albanski" lang="sq" hreflang="sq" data-title="Hapësira vektoriale" data-language-autonym="Shqip" data-language-local-name="albanski" 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 – srpski" lang="sr" hreflang="sr" data-title="Векторски простор" data-language-autonym="Српски / srpski" data-language-local-name="srpski" 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 – švedski" lang="sv" hreflang="sv" data-title="Linjärt rum" data-language-autonym="Svenska" data-language-local-name="švedski" 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 – tamilski" lang="ta" hreflang="ta" data-title="திசையன் வெளி" data-language-autonym="தமிழ்" data-language-local-name="tamilski" 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 – tagalog" lang="tl" hreflang="tl" data-title="Espasyong bektor" data-language-autonym="Tagalog" data-language-local-name="tagalog" 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 – turski" lang="tr" hreflang="tr" data-title="Vektör uzayı" data-language-autonym="Türkçe" data-language-local-name="turski" 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 – ukrajinski" lang="uk" hreflang="uk" data-title="Векторний простір" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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 – urdu" lang="ur" hreflang="ur" data-title="سمتیہ مکاں" data-language-autonym="اردو" data-language-local-name="urdu" 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 – venecijanski" lang="vec" hreflang="vec" data-title="Spasio vetorial" data-language-autonym="Vèneto" data-language-local-name="venecijanski" 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 – vijetnamski" lang="vi" hreflang="vi" data-title="Không gian vectơ" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" 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 – Wu kineski" lang="wuu" hreflang="wuu" data-title="向量空间" data-language-autonym="吴语" data-language-local-name="Wu kineski" 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 – kineski" lang="zh" hreflang="zh" data-title="向量空间" data-language-autonym="中文" data-language-local-name="kineski" 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 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="矢量空間" data-language-autonym="文言" data-language-local-name="Literary Chinese" 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 – Minnan" lang="nan" hreflang="nan" data-title="Hiòng-liōng khong-kan" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" 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 – 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data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</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">S Wikipedije, slobodne enciklopedije</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="bs" dir="ltr"><table class="plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Datoteka:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>Ovaj članak ili neki od njegovih odlomaka nije dovoljno potkrijepljen <a href="/wiki/Wikipedia:Provjerljivost" title="Wikipedia:Provjerljivost">izvorima</a></b> (literatura, veb-sajtovi ili drugi izvori).<span class="hide-when-compact"> Ako se pravilno ne potkrijepe <a href="/wiki/Wikipedia:Pouzdani_izvori" title="Wikipedia:Pouzdani izvori">pouzdanim</a> izvorima, sporne rečenice i navodi mogli bi biti izbrisani. Pomozite Wikipediji tako što ćete navesti validne izvore putem <a href="/wiki/Wikipedia:Citiranje_izvora" class="mw-redirect" title="Wikipedia:Citiranje izvora">referenci</a> te nakon toga možete ukloniti ovaj šablon.</span></div></td></tr></tbody></table> <p><b>Vektorski</b> ili <b>linearni prostor</b> je <a href="/wiki/Algebra" title="Algebra">algebarski</a> pojam u matematici koji nalazi primjenu u svim glavnim granama matematike, među kojima su <a href="/wiki/Linearna_algebra" title="Linearna algebra">linearna algebra</a>, <a href="/wiki/Matemati%C4%8Dka_analiza" title="Matematička analiza">analiza</a> i <a href="/w/index.php?title=Analiti%C4%8Dka_geometrija&action=edit&redlink=1" class="new" title="Analitička geometrija (stranica ne postoji)">analitička geometrija</a>. Definiše se na sljedeći način: </p><p>Neka skup <i>V</i> ima strukturu <a href="/w/index.php?title=Abelova_grupa&action=edit&redlink=1" class="new" title="Abelova grupa (stranica ne postoji)">Abelove grupe</a> u odnosu na <a href="/wiki/Sabiranje" title="Sabiranje">sabiranje</a>. Elemente skupa <i>V</i> zovemo <a href="/wiki/Vektor" class="mw-disambig" title="Vektor">vektori</a>. Neutralni element označujemo sa <i>0</i> i zovemo <i>nulti vektor</i>. </p><p>Neka skup <i>F</i> ima strukturu <a href="/w/index.php?title=Polje_(algebra)&action=edit&redlink=1" class="new" title="Polje (algebra) (stranica ne postoji)">polja</a>. Elemente skupa <i>F</i> zovemo <a href="/wiki/Skalar" class="mw-disambig" title="Skalar">skalari</a>, a neutralne elemente u odnosu na dvije binarne operacije označujemo sa <i>0</i> i <i>1</i>. </p><p>Na skupu <i>F × V</i> definirano je množenje vektora skalarom, tj. preslikavanje <i>F × V → V</i>, koje svakom skalaru <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 \alpha \in F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>∈</mo> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha \in F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79c9f26af61aa80c4a6cdbfcca784b79c4298099" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.069ex; height:2.176ex;" alt="{\displaystyle \alpha \in F}"></span> i svakom vektoru <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 x\in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa374e20b2db7f6b8caa71ff1865f7f84f215c9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.958ex; height:2.176ex;" alt="{\displaystyle x\in V}"></span> pridružuje vektor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha x\in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mi>x</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha x\in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f612268eb71bfb915631b99c94b6077fabc57574" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.445ex; height:2.176ex;" alt="{\displaystyle \alpha x\in V}"></span>, tako da vrijede sljedeći aksiomi: </p> <dl><dd><i><b>(I)</b></i> <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 \alpha (\beta x)=(\alpha \beta )x,\forall \alpha ,\beta \in F,\forall x\in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">(</mo> <mi>β</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mi>β</mi> <mo stretchy="false">)</mo> <mi>x</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha (\beta x)=(\alpha \beta )x,\forall \alpha ,\beta \in F,\forall x\in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dcbdc084d77e332f71c97cd554d1df1512b2e6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.061ex; height:2.843ex;" alt="{\displaystyle \alpha (\beta x)=(\alpha \beta )x,\forall \alpha ,\beta \in F,\forall x\in V}"></span></dd></dl> <dl><dd><i><b>(II)</b></i> <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 \alpha (x+y)=\alpha x+\alpha y,\forall \alpha \in F,\forall x,y\in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>α</mi> <mi>x</mi> <mo>+</mo> <mi>α</mi> <mi>y</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>α</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha (x+y)=\alpha x+\alpha y,\forall \alpha \in F,\forall x,y\in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d052975245c0c7b64eb8a7ecd4d0dbf99f2a376" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.891ex; height:2.843ex;" alt="{\displaystyle \alpha (x+y)=\alpha x+\alpha y,\forall \alpha \in F,\forall x,y\in V}"></span></dd></dl> <dl><dd><i><b>(III)</b></i> <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 (\alpha +\beta )x=\alpha x+\beta x,\forall \alpha ,\beta \in F,\forall x\in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mi>x</mi> <mo>=</mo> <mi>α</mi> <mi>x</mi> <mo>+</mo> <mi>β</mi> <mi>x</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>∈</mo> <mi>F</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\alpha +\beta )x=\alpha x+\beta x,\forall \alpha ,\beta \in F,\forall x\in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f6f9808dc534662ab1738e5226bce6d618285c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.262ex; height:2.843ex;" alt="{\displaystyle (\alpha +\beta )x=\alpha x+\beta x,\forall \alpha ,\beta \in F,\forall x\in V}"></span></dd></dl> <dl><dd><i><b>(IV)</b></i> <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 1x=x,\forall x\in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1x=x,\forall x\in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2fee774dceb34aeab530de4608480ee0fde45ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.204ex; height:2.509ex;" alt="{\displaystyle 1x=x,\forall x\in V}"></span></dd></dl> <p>Ovako se definisano preslikavanje zove <b>množenje vektora skalarom</b>, dok se <i>V</i> naziva <b>vektorski prostor</b> nad poljem <i>F</i> i piše <i>V(F)</i>. </p><p>Uobičajeno je da se vektorski prostori nad poljem realnih odnosno kompleksnih brojeva nazivaju realni, odnosno kompleksni vektorski prostori. Također, vektorski se prostor u kojem je definisan <a href="/w/index.php?title=Skalarni_produkt&action=edit&redlink=1" class="new" title="Skalarni produkt (stranica ne postoji)">skalarni produkt</a> naziva <a href="/wiki/Euklid" title="Euklid">Euklidski</a> vektorski prostor. </p> <div class="mw-heading mw-heading2"><h2 id="Također_pogledajte"><span id="Tako.C4.91er_pogledajte"></span>Također pogledajte</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vektorski_prostor&veaction=edit&section=1" title="Uredi odlomak "Također pogledajte"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vektorski_prostor&action=edit&section=1" title="Edit section's source code: Također pogledajte"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Spisak_vektorskih_identiteta" title="Spisak vektorskih 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algebra (stranica ne postoji)"><abbr title="Razgovor o šablonu" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">r</abbr></a></li><li class="nv-uredi"><a class="external text" href="https://bs.wikipedia.org/w/index.php?title=%C5%A0ablon:Linearna_algebra&action=edit"><abbr title="Uredi šablon" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">u</abbr></a></li></ul></div><div id="Linearna_algebra" style="font-size:114%;margin:0 4em"><a href="/wiki/Linearna_algebra" title="Linearna algebra">Linearna algebra</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Osnovni koncepti</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Skalar_(matematika)" title="Skalar (matematika)">Skalar</a></li> <li><a href="/wiki/Euklidski_vektor" title="Euklidski vektor">Vektor</a></li> 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nezavisnost</a></li> <li><a href="/w/index.php?title=Linearna_kombinacija&action=edit&redlink=1" class="new" title="Linearna kombinacija (stranica ne postoji)">Linearna kombinacija</a></li> <li><a href="/wiki/Baza_(linearna_algebra)" title="Baza (linearna algebra)">Baza</a></li> <li><a href="/w/index.php?title=Promjena_baze&action=edit&redlink=1" class="new" title="Promjena baze (stranica ne postoji)">Promjena baze</a></li> <li><a href="/w/index.php?title=Vektori_redova_i_kolona&action=edit&redlink=1" class="new" title="Vektori redova i kolona (stranica ne postoji)">Vektori redova i kolona</a></li> <li><a href="/w/index.php?title=Prostori_redova_i_kolona&action=edit&redlink=1" class="new" title="Prostori redova i kolona (stranica ne postoji)">Prostori redova i kolona</a></li> <li><a href="/w/index.php?title=Kernel_(linearna_algebra)&action=edit&redlink=1" class="new" title="Kernel (linearna algebra) (stranica ne postoji)">Kernel</a></li> <li><a href="/w/index.php?title=Svojstvene_vrijednosti_i_svojstveni_vektori&action=edit&redlink=1" class="new" title="Svojstvene vrijednosti i svojstveni vektori (stranica ne postoji)">Svojstvene vrijednosti i svojstveni vektori</a></li> <li><a href="/w/index.php?title=Transpozicija&action=edit&redlink=1" class="new" title="Transpozicija (stranica ne postoji)">Transpozicija</a></li> <li><a href="/wiki/Sistem_linearnih_jedna%C4%8Dina" title="Sistem linearnih jednačina">Linearne jednačine</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/Euklidov_prostor" title="Euklidov prostor"><img alt="Trodimenzionalni Euklidov prostor" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Linear_subspaces_with_shading.svg/80px-Linear_subspaces_with_shading.svg.png" decoding="async" width="80" height="58" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Linear_subspaces_with_shading.svg/120px-Linear_subspaces_with_shading.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Linear_subspaces_with_shading.svg/160px-Linear_subspaces_with_shading.svg.png 2x" data-file-width="325" data-file-height="236" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matrica_(matematika)" title="Matrica (matematika)">Matrice</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Blok_matrica&action=edit&redlink=1" class="new" title="Blok matrica (stranica ne postoji)">Blok</a></li> <li><a href="/w/index.php?title=Dekompozicija_matrice&action=edit&redlink=1" class="new" title="Dekompozicija matrice (stranica ne postoji)">Dekompozicija</a></li> <li><a href="/w/index.php?title=Invertibilna_matrica&action=edit&redlink=1" class="new" title="Invertibilna matrica (stranica ne postoji)">Invertibilna</a></li> <li><a href="/w/index.php?title=Minor_(linearna_algebra)&action=edit&redlink=1" class="new" title="Minor (linearna algebra) (stranica ne postoji)">Minor</a></li> <li><a href="/w/index.php?title=Mno%C5%BEenje_matrica&action=edit&redlink=1" class="new" title="Množenje matrica (stranica ne postoji)">Množenje</a></li> <li><a href="/w/index.php?title=Rang_(linearna_algebra)&action=edit&redlink=1" class="new" title="Rang (linearna algebra) (stranica ne postoji)">Rang</a></li> <li><a href="/w/index.php?title=Transformacijska_matrica&action=edit&redlink=1" class="new" title="Transformacijska matrica (stranica ne postoji)">Transformacija</a></li> <li><a href="/w/index.php?title=Cramerovo_pravilo&action=edit&redlink=1" class="new" title="Cramerovo pravilo (stranica ne postoji)">Cramerovo pravilo</a></li> <li><a href="/w/index.php?title=Gaussova_eliminacija&action=edit&redlink=1" class="new" title="Gaussova eliminacija (stranica ne postoji)">Gaussova eliminacija</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Bilinearno_preslikavanje&action=edit&redlink=1" class="new" title="Bilinearno preslikavanje (stranica ne postoji)">Bilinearno preslikavanje</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Ortogonalnost&action=edit&redlink=1" class="new" title="Ortogonalnost (stranica ne postoji)">Ortogonalnost</a></li> <li><a href="/wiki/Skalarni_proizvod" title="Skalarni proizvod">Skalarni proizvod</a></li> <li><a href="/w/index.php?title=Prostor_skalarnog_proizvoda&action=edit&redlink=1" class="new" title="Prostor skalarnog proizvoda (stranica ne postoji)">Prostor skalarnog proizvoda</a></li> <li><a href="/w/index.php?title=Vanjski_proizvod&action=edit&redlink=1" class="new" title="Vanjski proizvod (stranica ne postoji)">Vanjski proizvod</a></li> <li><a href="/w/index.php?title=Kroneckerov_proizvod&action=edit&redlink=1" class="new" title="Kroneckerov proizvod (stranica ne postoji)">Kroneckerov proizvod</a></li> <li><a href="/wiki/Gram%E2%80%93Schmidtov_postupak" title="Gram–Schmidtov postupak">Gram–Schmidtov postupak</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Multilinearna_algebra&action=edit&redlink=1" class="new" title="Multilinearna algebra (stranica ne postoji)">Multilinearna algebra</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Determinanta" title="Determinanta">Determinanta</a></li> <li><a href="/wiki/Vektorski_proizvod" title="Vektorski proizvod">Vektorski proizvod</a></li> <li><a href="/w/index.php?title=Trostruki_proizvod&action=edit&redlink=1" class="new" title="Trostruki proizvod (stranica ne postoji)">Trostruki proizvod</a></li> <li><a href="/w/index.php?title=Sedmodimenzionalni_vektorski_proizvod&action=edit&redlink=1" class="new" title="Sedmodimenzionalni vektorski proizvod (stranica ne postoji)">Sedmodimenzionalni vektorski proizvod</a></li> <li><a href="/w/index.php?title=Geometrijska_algebra&action=edit&redlink=1" class="new" title="Geometrijska algebra (stranica ne postoji)">Geometrijska algebra</a></li> <li><a href="/w/index.php?title=Eksterijerna_algebra&action=edit&redlink=1" class="new" title="Eksterijerna algebra (stranica ne postoji)">Eksterijerna algebra</a></li> <li><a href="/w/index.php?title=Bivektor&action=edit&redlink=1" class="new" title="Bivektor (stranica ne postoji)">Bivektor</a></li> <li><a href="/w/index.php?title=Multivektor&action=edit&redlink=1" class="new" title="Multivektor (stranica ne postoji)">Multivektor</a></li> <li><a href="/w/index.php?title=Tenzor&action=edit&redlink=1" class="new" title="Tenzor (stranica ne postoji)">Tenzor</a></li> <li><a href="/w/index.php?title=Vanjski_morfizam&action=edit&redlink=1" class="new" title="Vanjski morfizam (stranica ne postoji)">Vanjski morfizam</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Konstrukcije <a class="mw-selflink selflink">vektorskog prostora</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Dualni_prostor&action=edit&redlink=1" class="new" title="Dualni prostor (stranica ne postoji)">Dualni prostor</a></li> <li><a href="/w/index.php?title=Direktan_zbir_modula&action=edit&redlink=1" class="new" title="Direktan zbir modula (stranica ne postoji)">Direktan zbir</a></li> <li><a href="/w/index.php?title=Funkcijski_prostor&action=edit&redlink=1" class="new" title="Funkcijski prostor (stranica ne postoji)">Funkcijski prostor</a></li> <li><a href="/w/index.php?title=Kvocijentni_prostor_(linearna_algebra)&action=edit&redlink=1" class="new" title="Kvocijentni prostor (linearna algebra) (stranica ne postoji)">Kvocijentni prostor</a></li> <li><a href="/w/index.php?title=Linearni_podprostor&action=edit&redlink=1" class="new" title="Linearni podprostor (stranica ne postoji)">Podpostor</a></li> <li><a href="/w/index.php?title=Tenzorski_proizvod&action=edit&redlink=1" class="new" title="Tenzorski proizvod (stranica ne postoji)">Tenzorski proizvod</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=Numeri%C4%8Dka_linearna_algebra&action=edit&redlink=1" class="new" title="Numerička linearna algebra (stranica ne postoji)">Numerička</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Aritmetika_s_pokretnim_zarezom&action=edit&redlink=1" class="new" title="Aritmetika s pokretnim zarezom (stranica ne postoji)">Pokretni zarez</a></li> <li><a href="/w/index.php?title=Numeri%C4%8Dka_stabilnost&action=edit&redlink=1" class="new" title="Numerička stabilnost (stranica ne postoji)">Numerička stabilnost</a></li> <li><a href="/w/index.php?title=Osnovni_potprogrami_linearne_algebre&action=edit&redlink=1" class="new" title="Osnovni potprogrami linearne algebre (stranica ne postoji)">Basic Linear Algebra Subprograms (BLAS)</a></li> <li><a href="/w/index.php?title=Prorije%C4%91ena_matrica&action=edit&redlink=1" class="new" title="Prorijeđena matrica (stranica ne postoji)">Prorijeđena matrica</a></li> <li><a href="/w/index.php?title=Pore%C4%91enje_biblioteka_linearne_algebre&action=edit&redlink=1" class="new" 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