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<input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Prijedi na druge jezične varijante članka. Dostupno je na 28 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-28" 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">28 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%A8%D8%B1%D9%87%D9%86%D8%A9_%D9%83%D8%A7%D9%8A%D9%84%D9%8A-%D9%87%D8%A7%D9%85%D9%8A%D9%84%D8%AA%D9%88%D9%86" title="مبرهنة كايلي-هاميلتون — Arapski" lang="ar" hreflang="ar" data-title="مبرهنة كايلي-هاميلتون" data-language-autonym="العربية" data-language-local-name="Arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%87%E0%A6%B2%E0%A6%BF%E2%80%93%E0%A6%B9%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%B2%E0%A7%8D%E0%A6%9F%E0%A6%A8_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="কেলি–হ্যামিল্টন তত্ত্ব — Bengalski" lang="bn" hreflang="bn" data-title="কেলি–হ্যামিল্টন তত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="Bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Cayley-Hamiltonova_teorema" title="Cayley-Hamiltonova teorema — Bosanski" lang="bs" hreflang="bs" data-title="Cayley-Hamiltonova teorema" data-language-autonym="Bosanski" data-language-local-name="Bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teorema_de_Cayley-Hamilton" title="Teorema de Cayley-Hamilton — Katalonski" lang="ca" hreflang="ca" data-title="Teorema de Cayley-Hamilton" data-language-autonym="Català" data-language-local-name="Katalonski" 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/Cayleyho%E2%80%93Hamiltonova_v%C4%9Bta" title="Cayleyho–Hamiltonova věta — Češki" lang="cs" hreflang="cs" data-title="Cayleyho–Hamiltonova věta" data-language-autonym="Čeština" data-language-local-name="Češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Satz_von_Cayley-Hamilton" title="Satz von Cayley-Hamilton — Nemački" lang="de" hreflang="de" data-title="Satz von Cayley-Hamilton" data-language-autonym="Deutsch" data-language-local-name="Nemački" 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%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%9A%CE%AD%CE%B9%CE%BB%CE%B9-%CE%A7%CE%AC%CE%BC%CE%B9%CE%BB%CF%84%CE%BF%CE%BD" title="Θεώρημα Κέιλι-Χάμιλτον — Grčki" lang="el" hreflang="el" data-title="Θεώρημα Κέιλι-Χάμιλτον" data-language-autonym="Ελληνικά" data-language-local-name="Grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem" title="Cayley–Hamilton theorem — Engleski" lang="en" hreflang="en" data-title="Cayley–Hamilton theorem" data-language-autonym="English" data-language-local-name="Engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teorema_de_Cayley-Hamilton" title="Teorema de Cayley-Hamilton — Španski" lang="es" hreflang="es" data-title="Teorema de Cayley-Hamilton" data-language-autonym="Español" data-language-local-name="Španski" 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/%D9%82%D8%B6%DB%8C%D9%87_%DA%A9%DB%8C%D9%84%DB%8C-%D9%87%D9%85%DB%8C%D9%84%D8%AA%D9%88%D9%86" title="قضیه کیلی-همیلتون — Persijski" lang="fa" hreflang="fa" data-title="قضیه کیلی-همیلتون" data-language-autonym="فارسی" data-language-local-name="Persijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Cayley-Hamilton" title="Théorème de Cayley-Hamilton — Francuski" lang="fr" hreflang="fr" data-title="Théorème de Cayley-Hamilton" data-language-autonym="Français" data-language-local-name="Francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%A7%D7%99%D7%99%D7%9C%D7%99-%D7%94%D7%9E%D7%99%D7%9C%D7%98%D7%95%D7%9F" title="משפט קיילי-המילטון — Hebrejski" lang="he" hreflang="he" data-title="משפט קיילי-המילטון" data-language-autonym="עברית" data-language-local-name="Hebrejski" 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/Cayley-Hamiltonov_teorem" title="Cayley-Hamiltonov teorem — Hrvatski" lang="hr" hreflang="hr" data-title="Cayley-Hamiltonov teorem" 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/Cayley%E2%80%93Hamilton-t%C3%A9tel" title="Cayley–Hamilton-tétel — Mađarski" lang="hu" hreflang="hu" data-title="Cayley–Hamilton-tétel" data-language-autonym="Magyar" data-language-local-name="Mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teorema_di_Hamilton-Cayley" title="Teorema di Hamilton-Cayley — Italijanski" lang="it" hreflang="it" data-title="Teorema di Hamilton-Cayley" 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%82%B1%E3%82%A4%E3%83%AA%E3%83%BC%E3%83%BB%E3%83%8F%E3%83%9F%E3%83%AB%E3%83%88%E3%83%B3%E3%81%AE%E5%AE%9A%E7%90%86" title="ケイリー・ハミルトンの定理 — Japanski" lang="ja" hreflang="ja" data-title="ケイリー・ハミルトンの定理" 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/%EC%BC%80%EC%9D%BC%EB%A6%AC-%ED%95%B4%EB%B0%80%ED%84%B4_%EC%A0%95%EB%A6%AC" title="케일리-해밀턴 정리 — Korejski" lang="ko" hreflang="ko" data-title="케일리-해밀턴 정리" data-language-autonym="한국어" data-language-local-name="Korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Stelling_van_Cayley-Hamilton" title="Stelling van Cayley-Hamilton — Holandski" lang="nl" hreflang="nl" data-title="Stelling van Cayley-Hamilton" data-language-autonym="Nederlands" data-language-local-name="Holandski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Twierdzenie_Cayleya-Hamiltona" title="Twierdzenie Cayleya-Hamiltona — Poljski" lang="pl" hreflang="pl" data-title="Twierdzenie Cayleya-Hamiltona" data-language-autonym="Polski" data-language-local-name="Poljski" 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/Teorema_de_Cayley-Hamilton" title="Teorema de Cayley-Hamilton — Portugalski" lang="pt" hreflang="pt" data-title="Teorema de Cayley-Hamilton" data-language-autonym="Português" data-language-local-name="Portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teorema_Cayley-Hamilton" title="Teorema Cayley-Hamilton — Rumunski" lang="ro" hreflang="ro" data-title="Teorema Cayley-Hamilton" 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%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%93%D0%B0%D0%BC%D0%B8%D0%BB%D1%8C%D1%82%D0%BE%D0%BD%D0%B0_%E2%80%94_%D0%9A%D1%8D%D0%BB%D0%B8" title="Теорема Гамильтона — Кэли — Ruski" lang="ru" hreflang="ru" data-title="Теорема Гамильтона — Кэли" data-language-autonym="Русский" data-language-local-name="Ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Cayleyho-Hamiltonova_veta" title="Cayleyho-Hamiltonova veta — Slovački" lang="sk" hreflang="sk" data-title="Cayleyho-Hamiltonova veta" data-language-autonym="Slovenčina" data-language-local-name="Slovački" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B5%D1%98%D0%BB%D0%B8-%D0%A5%D0%B0%D0%BC%D0%B8%D0%BB%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0" title="Кејли-Хамилтонова теорема — Srpski" lang="sr" hreflang="sr" data-title="Кејли-Хамилтонова теорема" 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/Cayley%E2%80%93Hamiltons_sats" title="Cayley–Hamiltons sats — Švedski" lang="sv" hreflang="sv" data-title="Cayley–Hamiltons sats" data-language-autonym="Svenska" data-language-local-name="Švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%93%D0%B0%D0%BC%D1%96%D0%BB%D1%8C%D1%82%D0%BE%D0%BD%D0%B0_%E2%80%94_%D0%9A%D0%B5%D0%BB%D1%96" title="Теорема Гамільтона — Келі — Ukrajinski" lang="uk" hreflang="uk" data-title="Теорема Гамільтона — Келі" 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/%DA%A9%DB%8C%D9%84%DB%92_%DB%81%D9%85%DB%8C%D9%84%D9%B9%D9%86_%D9%85%D8%B3%D8%A6%D9%84%DB%81_%D8%A7%D8%AB%D8%A8%D8%A7%D8%AA%DB%8C" title="کیلے ہمیلٹن مسئلہ اثباتی — Urdu" lang="ur" hreflang="ur" data-title="کیلے ہمیلٹن مسئلہ اثباتی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%87%B1%E8%90%8A%E2%80%93%E5%93%88%E5%AF%86%E9%A0%93%E5%AE%9A%E7%90%86" title="凱萊–哈密頓定理 — Kineski" lang="zh" hreflang="zh" data-title="凱萊–哈密頓定理" data-language-autonym="中文" data-language-local-name="Kineski" class="interlanguage-link-target"><span>中文</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/Q656772#sitelinks-wikipedia" title="Uredi međujezične poveznice" class="wbc-editpage">Uredi veze</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" lang="sh-Latn" dir="ltr"> <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/Cayley-Hamiltonov_teorem" title="Vidi stranicu sadržaja [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Cayley-Hamiltonov_teorem&action=edit&redlink=1" rel="discussion" class="new" title="Razgovarajte o sadržini ove stranice (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " lang="sh-Latn" dir="ltr"> <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="Promijeni jezičnu varijantu" > <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" 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Teorem glasi:</div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>'''Cayley-Hamiltonov teorem'''<ins class="diffchange diffchange-inline"> ([[hrvatski jezik|hrv.]]) ili '''Kejli-Hamiltonova teorema''' ([[srpski jezik|srp.]])</ins> je <ins class="diffchange diffchange-inline">jedna</ins> od najznačajnijih tvrdnji u [[linearna algebra|linearnoj algebri]]. Teorem glasi:</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>:''Svaka kvadratna matrica poništava svoj [[karakteristični polinom]].''</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>:''Svaka kvadratna matrica poništava svoj [[karakteristični polinom]].''</div></td> </tr> <tr> <td colspan="2" class="diff-lineno">Red 20:</td> <td colspan="2" class="diff-lineno">Red 20:</td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>[[Kategorija:Linearna algebra]]</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>[[Kategorija:Linearna algebra]]</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ar:مبرهنة كايلي-هاميلتون]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[bs:Cayley-Hamiltonov teorem]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ca:Teorema de Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[cs:Cayleyho-Hamiltonova věta]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[de:Satz von Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[en:Cayley–Hamilton theorem]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[es:Teorema de Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[fr:Théorème de Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[he:משפט קיילי-המילטון]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[hr:Cayley-Hamiltonov teorem]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[hu:Cayley–Hamilton-tétel]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[it:Teorema di Hamilton-Cayley]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ja:ケイリー・ハミルトンの定理]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ko:케일리-해밀턴 정리]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[nl:Stelling van Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[pl:Twierdzenie Cayleya-Hamiltona]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[pt:Teorema de Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ro:Teorema Cayley-Hamilton]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ru:Теорема Гамильтона — Кэли]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[sk:Cayleyho-Hamiltonova veta]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[sr:Кејли-Хамилтонова теорема]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[sv:Cayley-Hamiltons sats]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[uk:Теорема Гамільтона — Келі]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[ur:کیلے ہمیلٹن مسلئہ اثباتی]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>[[zh:凱萊－哈密頓定理]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Aktualna verzija od 18. septembra 2013. u 21:37</h2> <div class="mw-content-ltr mw-parser-output" lang="sh-Latn" dir="ltr"><p><b>Cayley-Hamiltonov teorem</b> (<a href="/wiki/Hrvatski_jezik" title="Hrvatski jezik">hrv.</a>) ili <b>Kejli-Hamiltonova teorema</b> (<a href="/wiki/Srpski_jezik" title="Srpski jezik">srp.</a>) je jedna od najznačajnijih tvrdnji u <a href="/wiki/Linearna_algebra" title="Linearna algebra">linearnoj algebri</a>. Teorem glasi: </p> <dl><dd><i>Svaka kvadratna matrica poništava svoj <a href="/wiki/Karakteristi%C4%8Dni_polinom" title="Karakteristični polinom">karakteristični polinom</a>.</i></dd></dl> <p>Promotrimo na primjer <a href="/wiki/Matrica_(matematika)" title="Matrica (matematika)">matricu</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\begin{bmatrix}1&2\\3&4\end{bmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\begin{bmatrix}1&2\\3&4\end{bmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2ad022957cb84bddcab9e9ed7c0828bc28c3aba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:13.342ex; height:6.176ex;" alt="{\displaystyle A={\begin{bmatrix}1&2\\3&4\end{bmatrix}}.}"></span></dd></dl> <p>Njen karakteristični polinom je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(\lambda )={\begin{vmatrix}\lambda -1&-2\\-3&\lambda -4\end{vmatrix}}=(\lambda -1)(\lambda -4)-2\cdot 3=\lambda ^{2}-5\lambda -2.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>λ</mi> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mo>−</mo> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>3</mn> </mtd> <mtd> <mi>λ</mi> <mo>−</mo> <mn>4</mn> </mtd> </mtr> </mtable> <mo>|</mo> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>−</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>−</mo> <mn>2</mn> <mo>⋅</mo> <mn>3</mn> <mo>=</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>5</mn> <mi>λ</mi> <mo>−</mo> <mn>2.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(\lambda )={\begin{vmatrix}\lambda -1&-2\\-3&\lambda -4\end{vmatrix}}=(\lambda -1)(\lambda -4)-2\cdot 3=\lambda ^{2}-5\lambda -2.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/407521631f4a6e984f879d8fda289d7c519d7472" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.089ex; width:62.399ex; height:6.176ex;" alt="{\displaystyle p(\lambda )={\begin{vmatrix}\lambda -1&-2\\-3&\lambda -4\end{vmatrix}}=(\lambda -1)(\lambda -4)-2\cdot 3=\lambda ^{2}-5\lambda -2.}"></span></dd></dl> <p>A u saglasnosti s Cayley-Hamiltonovim teoremom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{2}-5A-2I_{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>5</mn> <mi>A</mi> <mo>−</mo> <mn>2</mn> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{2}-5A-2I_{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1ac033638d8c0b302772e842c0eb2b4c0726e25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.884ex; height:3.009ex;" alt="{\displaystyle A^{2}-5A-2I_{2}=0}"></span></dd></dl> <div class="boilerplate metadata" id="stub"><table cellpadding="0" cellspacing="0" style="background-color: transparent"><tbody><tr><td><span typeof="mw:File"><a href="/wiki/Datoteka:E-to-the-i-pi.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/35px-E-to-the-i-pi.svg.png" decoding="async" width="35" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/53px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/70px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td><td><i> Ovaj članak o <b>matematici</b> je <a href="/wiki/Wikipedija:%C4%8Clanci_u_za%C4%8Detku" title="Wikipedija:Članci u začetku">u začetku</a>. 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