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Je dostupný v 36 jazykoch" > <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-36" 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">36 jazykov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B1%D9%83%D9%8A%D8%A8_%D8%AE%D8%B7%D9%8A" title="تركيب خطي – arabčina" lang="ar" hreflang="ar" data-title="تركيب خطي" data-language-autonym="العربية" data-language-local-name="arabčina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Combinaci%C3%B3_lineal" title="Combinació lineal – katalánčina" lang="ca" hreflang="ca" data-title="Combinació lineal" data-language-autonym="Català" data-language-local-name="katalánčina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Line%C3%A1rn%C3%AD_kombinace" title="Lineární kombinace – čeština" lang="cs" hreflang="cs" data-title="Lineární kombinace" data-language-autonym="Čeština" data-language-local-name="čeština" 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%9B%D0%B8%D0%BD%D0%B8%D0%BB%D0%BB%D0%B5_%D0%BA%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%86%D0%B8" title="Линилле комбинаци – čuvaština" lang="cv" hreflang="cv" data-title="Линилле комбинаци" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Linearkombination" title="Linearkombination – nemčina" lang="de" hreflang="de" data-title="Linearkombination" data-language-autonym="Deutsch" data-language-local-name="nemčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Linear_combination" title="Linear combination – angličtina" lang="en" hreflang="en" data-title="Linear combination" data-language-autonym="English" data-language-local-name="angličtina" 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/Lineara_kombina%C4%B5o" title="Lineara kombinaĵo – esperanto" lang="eo" hreflang="eo" data-title="Lineara kombinaĵo" 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/Combinaci%C3%B3n_lineal" title="Combinación lineal – španielčina" lang="es" hreflang="es" data-title="Combinación lineal" data-language-autonym="Español" data-language-local-name="španielčina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%B1%DA%A9%DB%8C%D8%A8_%D8%AE%D8%B7%DB%8C" title="ترکیب خطی – perzština" lang="fa" hreflang="fa" data-title="ترکیب خطی" data-language-autonym="فارسی" data-language-local-name="perzština" 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/Lineaarikombinaatio" title="Lineaarikombinaatio – fínčina" lang="fi" hreflang="fi" data-title="Lineaarikombinaatio" data-language-autonym="Suomi" data-language-local-name="fínčina" 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/Combinaison_lin%C3%A9aire" title="Combinaison linéaire – francúzština" lang="fr" hreflang="fr" data-title="Combinaison linéaire" data-language-autonym="Français" data-language-local-name="francúzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Combinaci%C3%B3n_linear" title="Combinación linear – galícijčina" lang="gl" hreflang="gl" data-title="Combinación linear" data-language-autonym="Galego" data-language-local-name="galícijčina" 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%A6%D7%99%D7%A8%D7%95%D7%A3_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99" title="צירוף ליניארי – hebrejčina" lang="he" hreflang="he" data-title="צירוף ליניארי" data-language-autonym="עברית" data-language-local-name="hebrejčina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Linearna_kombinacija" title="Linearna kombinacija – chorvátčina" lang="hr" hreflang="hr" data-title="Linearna kombinacija" data-language-autonym="Hrvatski" data-language-local-name="chorvátčina" 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/Line%C3%A1ris_kombin%C3%A1ci%C3%B3" title="Lineáris kombináció – maďarčina" lang="hu" hreflang="hu" data-title="Lineáris kombináció" data-language-autonym="Magyar" data-language-local-name="maďarčina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kombinasi_linear" title="Kombinasi linear – indonézština" lang="id" hreflang="id" data-title="Kombinasi linear" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonézština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Combinazione_lineare" title="Combinazione lineare – taliančina" lang="it" hreflang="it" data-title="Combinazione lineare" data-language-autonym="Italiano" data-language-local-name="taliančina" 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/%E7%B7%9A%E5%9E%8B%E7%B5%90%E5%90%88" title="線型結合 – japončina" lang="ja" hreflang="ja" data-title="線型結合" data-language-autonym="日本語" data-language-local-name="japončina" 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/%EC%84%A0%ED%98%95_%EA%B2%B0%ED%95%A9" title="선형 결합 – kórejčina" lang="ko" hreflang="ko" data-title="선형 결합" data-language-autonym="한국어" data-language-local-name="kórejčina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B0%E0%B5%87%E0%B4%96%E0%B5%80%E0%B4%AF%E0%B4%B8%E0%B4%9E%E0%B5%8D%E0%B4%9A%E0%B4%AF%E0%B4%82" title="രേഖീയസഞ്ചയം – malajálamčina" lang="ml" hreflang="ml" data-title="രേഖീയസഞ്ചയം" data-language-autonym="മലയാളം" data-language-local-name="malajálamčina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Lineaire_combinatie" title="Lineaire combinatie – holandčina" lang="nl" hreflang="nl" data-title="Lineaire combinatie" data-language-autonym="Nederlands" data-language-local-name="holandčina" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Line%C3%A6rkombinasjon" title="Lineærkombinasjon – nórčina (bokmal)" lang="nb" hreflang="nb" data-title="Lineærkombinasjon" data-language-autonym="Norsk bokmål" data-language-local-name="nórčina (bokmal)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kombinacja_liniowa" title="Kombinacja liniowa – poľština" lang="pl" hreflang="pl" data-title="Kombinacja liniowa" data-language-autonym="Polski" data-language-local-name="poľština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Combina%C3%A7%C3%A3o_linear" title="Combinação linear – portugalčina" lang="pt" hreflang="pt" data-title="Combinação linear" data-language-autonym="Português" data-language-local-name="portugalčina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D0%BA%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%86%D0%B8%D1%8F" title="Линейная комбинация – ruština" lang="ru" hreflang="ru" data-title="Линейная комбинация" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Linear_combination" title="Linear combination – Simple English" lang="en-simple" hreflang="en-simple" data-title="Linear combination" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Linearna_kombinacija" title="Linearna kombinacija – slovinčina" lang="sl" hreflang="sl" data-title="Linearna kombinacija" data-language-autonym="Slovenščina" data-language-local-name="slovinčina" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Linj%C3%A4rkombination" title="Linjärkombination – švédčina" lang="sv" hreflang="sv" data-title="Linjärkombination" data-language-autonym="Svenska" data-language-local-name="švédčina" 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%A8%E0%AF%87%E0%AE%B0%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D_%E0%AE%9A%E0%AF%87%E0%AE%B0%E0%AF%8D%E0%AE%B5%E0%AF%81" title="நேரியல் சேர்வு – tamilčina" lang="ta" hreflang="ta" data-title="நேரியல் சேர்வு" data-language-autonym="தமிழ்" data-language-local-name="tamilčina" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9C%E0%B8%A5%E0%B8%A3%E0%B8%A7%E0%B8%A1%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B9%80%E0%B8%AA%E0%B9%89%E0%B8%99" title="ผลรวมเชิงเส้น – thajčina" lang="th" hreflang="th" data-title="ผลรวมเชิงเส้น" data-language-autonym="ไทย" data-language-local-name="thajčina" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Do%C4%9Frusal_birle%C5%9Fim" title="Doğrusal birleşim – turečtina" lang="tr" hreflang="tr" data-title="Doğrusal birleşim" data-language-autonym="Türkçe" data-language-local-name="turečtina" 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%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%BA%D0%BE%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%86%D1%96%D1%8F" title="Лінійна комбінація – ukrajinčina" lang="uk" hreflang="uk" data-title="Лінійна комбінація" data-language-autonym="Українська" data-language-local-name="ukrajinčina" 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%AE%D8%B7%DB%8C_%D8%A7%D8%AC%D8%AA%D9%85%D8%A7%D8%B9" title="خطی اجتماع – urdčina" lang="ur" hreflang="ur" data-title="خطی اجتماع" data-language-autonym="اردو" data-language-local-name="urdčina" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BB%95_h%E1%BB%A3p_tuy%E1%BA%BFn_t%C3%ADnh" title="Tổ hợp tuyến tính – vietnamčina" lang="vi" hreflang="vi" data-title="Tổ hợp tuyến tính" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamčina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88" title="线性组合 – čínština" lang="zh" hreflang="zh" data-title="线性组合" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B7%9A%E6%80%A7%E7%B5%84%E5%90%88" title="線性組合 – kantončina" lang="yue" hreflang="yue" data-title="線性組合" data-language-autonym="粵語" data-language-local-name="kantončina" 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/Q27628#sitelinks-wikipedia" title="Upraviť medzijazykové odkazy" class="wbc-editpage">Upraviť odkazy</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="Menné priestory"> <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/Line%C3%A1rna_kombin%C3%A1cia" title="Zobraziť obsah stránky [c]" accesskey="c"><span>Stránka</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskusia:Line%C3%A1rna_kombin%C3%A1cia&action=edit&redlink=1" rel="discussion" class="new" title="Diskusia o obsahu stránky (stránka neexistuje) [t]" accesskey="t"><span>Diskusia</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="Změnit variantu jazyka" > <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">slovenčina</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="Zobrazenia"> <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/Line%C3%A1rna_kombin%C3%A1cia"><span>Čítať</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&veaction=edit" title="Upraviť túto stránku [v]" accesskey="v"><span>Upraviť</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=edit" title="Upraviť zdrojový kód tejto stránky [e]" accesskey="e"><span>Upraviť zdroj</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=history" title="Minulé revízie tejto stránky. [h]" accesskey="h"><span>Zobraziť históriu</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Nástroje stránky"> <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="Nástroje" > <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">Nástroje</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">Nástroje</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">presunúť do postranného panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skryť</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Další možnosti" > <div class="vector-menu-heading"> Akcie </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/Line%C3%A1rna_kombin%C3%A1cia"><span>Čítať</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&veaction=edit" title="Upraviť túto stránku [v]" accesskey="v"><span>Upraviť</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=edit" title="Upraviť zdrojový kód tejto stránky [e]" accesskey="e"><span>Upraviť zdroj</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=history"><span>Zobraziť históriu</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Všeobecné </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%C5%A0peci%C3%A1lne:%C4%8CoOdkazujeSem/Line%C3%A1rna_kombin%C3%A1cia" title="Zoznam všetkých wiki stránok, ktoré sem odkazujú [j]" accesskey="j"><span>Odkazy na túto stránku</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%C5%A0peci%C3%A1lne:S%C3%BAvisiacePosledn%C3%A9%C3%9Apravy/Line%C3%A1rna_kombin%C3%A1cia" rel="nofollow" title="Posledné úpravy na stránkach, na ktoré odkazuje táto stránka [k]" accesskey="k"><span>Súvisiace úpravy</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=sk" title="Nahranie súborov [u]" accesskey="u"><span>Nahrať súbor</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%C5%A0peci%C3%A1lne:%C5%A0peci%C3%A1lneStr%C3%A1nky" title="Zoznam všetkých špeciálnych stránok [q]" accesskey="q"><span>Špeciálne stránky</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&oldid=7391051" title="Trvalý odkaz na túto verziu stránky"><span>Trvalý odkaz</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=info" title="Viac informácií o tejto stránke"><span>Informácie o stránke</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%C5%A0peci%C3%A1lne:Citova%C5%A5&page=Line%C3%A1rna_kombin%C3%A1cia&id=7391051&wpFormIdentifier=titleform" title="Informácie ako citovať túto stránku"><span>Citovať túto stránku</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%C5%A0peci%C3%A1lne:UrlShortener&url=https%3A%2F%2Fsk.wikipedia.org%2Fwiki%2FLine%25C3%25A1rna_kombin%25C3%25A1cia"><span>Získať skrátené URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%C5%A0peci%C3%A1lne:QrCode&url=https%3A%2F%2Fsk.wikipedia.org%2Fwiki%2FLine%25C3%25A1rna_kombin%25C3%25A1cia"><span>Stiahnuť QR kód</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"> Tlačiť/exportovať </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=%C5%A0peci%C3%A1lne:Knihy&bookcmd=book_creator&referer=Line%C3%A1rna+kombin%C3%A1cia"><span>Vytvoriť knihu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%C5%A0peci%C3%A1lne:DownloadAsPdf&page=Line%C3%A1rna_kombin%C3%A1cia&action=show-download-screen"><span>Stiahnuť ako PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&printable=yes" title="Verzia tejto stránky pre tlač [p]" accesskey="p"><span>Verzia pre tlač</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> V iných projektoch </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q27628" title="Odkaz na prepojenú položku dátového úložiska [g]" accesskey="g"><span>Položka Wikidata</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="Nástroje stránky"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Vzhľad"> <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">Vzhľad</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">presunúť do postranného panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skryť</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">z Wikipédie, slobodnej encyklopédie</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="sk" dir="ltr"><p><b>Lineárnou kombináciou</b> prvkov (<a href="/wiki/Vektor_(matematika)" title="Vektor (matematika)">vektorov</a>) vektorového priestoru rozumieme nový prvok (vektor), ktorý tomuto priestoru taktiež náleží. Vektorový priestor je generovaný jeho bázovými vektormi. Každý prvok tohto priestoru sa teda dá vyjadriť ako lineárna kombinácia jeho bázových vektorov. </p> <div class="mw-heading mw-heading2"><h2 id="Definícia"><span id="Defin.C3.ADcia"></span>Definícia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&veaction=edit&section=1" title="Upraviť sekciu: Definícia" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=edit&section=1" title="Editovat zdrojový kód sekce Definícia"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nech <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 {\mathcal {V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">V</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47d69f309b6deb2e5008f6130ee11e09bbabd7b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.529ex; height:2.176ex;" alt="{\displaystyle {\mathcal {V}}}"></span> je vektorový priestor nad poľom <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 \mathbb {K} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">K</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {K} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1848c435e64864e9ad4efa7e46bd6bc900c35c99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {K} }"></span>. Nech <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 \{c_{j},j=1,2,\cdots ,n\}\subset \mathbb {K} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>n</mi> <mo fence="false" stretchy="false">}</mo> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">K</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{c_{j},j=1,2,\cdots ,n\}\subset \mathbb {K} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98e52afeb4e0c473b7c5a084c7eda3f49c694c9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.17ex; height:3.009ex;" alt="{\displaystyle \{c_{j},j=1,2,\cdots ,n\}\subset \mathbb {K} }"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{\mathbf {v} _{j},j=1,2,\cdots ,n\}\subset {\mathcal {V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>n</mi> <mo fence="false" stretchy="false">}</mo> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">V</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{\mathbf {v} _{j},j=1,2,\cdots ,n\}\subset {\mathcal {V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f25b724270d90dbe347a4f2fa3b57cf0dc0d983e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.296ex; height:3.009ex;" alt="{\displaystyle \{\mathbf {v} _{j},j=1,2,\cdots ,n\}\subset {\mathcal {V}}}"></span>. Potom lineárnou kombináciou <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 {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {v} }"></span> rozumieme vektor<br /> </p> <dl><dd><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 {v} =\sum _{j=1}^{n}c_{j}\mathbf {v} _{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} =\sum _{j=1}^{n}c_{j}\mathbf {v} _{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b8c8dcea4c04362b7ecc061239d7652ebaf991a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:12.489ex; height:7.176ex;" alt="{\displaystyle \mathbf {v} =\sum _{j=1}^{n}c_{j}\mathbf {v} _{j}}"></span></dd></dl></dd></dl> <p>Vektormi nemusíme nutne chápať n-tice čísel, ale aj funkcie a iné matematické objekty. Napríklad lineárnou kombináciou na priestore polynómov je nový polynóm </p> <dl><dd><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 f=\sum _{j=1}^{n}c_{j}f_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=\sum _{j=1}^{n}c_{j}f_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16f5da2531c16c048465fd8608518d3152daff33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:12.085ex; height:7.176ex;" alt="{\displaystyle f=\sum _{j=1}^{n}c_{j}f_{j}}"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Príklad"><span id="Pr.C3.ADklad"></span>Príklad</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&veaction=edit&section=2" title="Upraviť sekciu: Príklad" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Line%C3%A1rna_kombin%C3%A1cia&action=edit&section=2" title="Editovat zdrojový kód sekce Príklad"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sú dané lineárne nezávislé polynómy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{1}(x)=x^{2}-x,\,f_{2}(x)=x+2,\,f_{3}(x)=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>x</mi> <mo>,</mo> <mspace width="thinmathspace" /> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mo>,</mo> <mspace width="thinmathspace" /> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{1}(x)=x^{2}-x,\,f_{2}(x)=x+2,\,f_{3}(x)=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d45bafd02d7c0f34f567d41a5d6642ada163637b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.184ex; height:3.176ex;" alt="{\displaystyle f_{1}(x)=x^{2}-x,\,f_{2}(x)=x+2,\,f_{3}(x)=1}"></span>. Lineárnu kombináciu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{2}+4x+4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{2}+4x+4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79f5b85b962b6303265ea5168ca45418a7a1b9b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.235ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{2}+4x+4}"></span> dosiahneme voľbou<br /> </p> <dl><dd><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 f=1\cdot f_{1}+5\cdot f_{2}-6\cdot f_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mn>1</mn> <mo>⋅</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>5</mn> <mo>⋅</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <mn>6</mn> <mo>⋅</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=1\cdot f_{1}+5\cdot f_{2}-6\cdot f_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b596c04ceeb54a5ffe24fd1f96bdb115ef2885f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.163ex; height:2.509ex;" alt="{\displaystyle f=1\cdot f_{1}+5\cdot f_{2}-6\cdot f_{3}}"></span></dd></dl></dd></dl> <p><br /> </p> <div role="navigation" class="navbox" aria-labelledby="Lineárna_algebra" style="padding:3px"><table class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/%C5%A0abl%C3%B3na:Line%C3%A1rna_algebra" title="Šablóna:Lineárna algebra"><span title="Zobraz túto šablónu" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">z</span></a></li><li class="nv-talk"><a href="/w/index.php?title=Diskusia_k_%C5%A1abl%C3%B3ne:Line%C3%A1rna_algebra&action=edit&redlink=1" class="new" title="Diskusia k šablóne:Lineárna algebra (stránka 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