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Available in 17 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-17" 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">17 gjuhë</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Jedni%C4%8Dkov%C3%A1_matice" title="Jedničková matice – çekisht" lang="cs" hreflang="cs" data-title="Jedničková matice" data-language-autonym="Čeština" data-language-local-name="çekisht" 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%9F%C4%95%D1%80%D1%80%D0%B5%D1%81%D0%B5%D0%BD_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B8" title="Пĕрресен матрици – çuvashisht" lang="cv" hreflang="cv" data-title="Пĕрресен матрици" data-language-autonym="Чӑвашла" data-language-local-name="çuvashisht" 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/Einsmatrix" title="Einsmatrix – gjermanisht" lang="de" hreflang="de" data-title="Einsmatrix" data-language-autonym="Deutsch" data-language-local-name="gjermanisht" 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%A0%CE%AF%CE%BD%CE%B1%CE%BA%CE%B1%CF%82_%CE%B1%CF%80%CF%8C_%CE%BC%CE%BF%CE%BD%CE%AC%CE%B4%CE%B5%CF%82" title="Πίνακας από μονάδες – greqisht" lang="el" hreflang="el" data-title="Πίνακας από μονάδες" data-language-autonym="Ελληνικά" data-language-local-name="greqisht" 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/Matrix_of_ones" title="Matrix of ones – anglisht" lang="en" hreflang="en" data-title="Matrix of ones" data-language-autonym="English" data-language-local-name="anglisht" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%A7%D8%AA%D8%B1%DB%8C%D8%B3_%DB%8C%DA%A9%E2%80%8C%D9%87%D8%A7" title="ماتریس یک‌ها – persisht" lang="fa" hreflang="fa" data-title="ماتریس یک‌ها" data-language-autonym="فارسی" data-language-local-name="persisht" 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/Ykk%C3%B6smatriisi" title="Ykkösmatriisi – finlandisht" lang="fi" hreflang="fi" data-title="Ykkösmatriisi" data-language-autonym="Suomi" data-language-local-name="finlandisht" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Matriz_de_uns" title="Matriz de uns – galicisht" lang="gl" hreflang="gl" data-title="Matriz de uns" data-language-autonym="Galego" data-language-local-name="galicisht" 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%98%D7%A8%D7%99%D7%A6%D7%AA_%D7%90%D7%97%D7%93%D7%95%D7%AA" title="מטריצת אחדות – hebraisht" lang="he" hreflang="he" data-title="מטריצת אחדות" data-language-autonym="עברית" data-language-local-name="hebraisht" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Matrice_cu_toate_elementele_1" title="Matrice cu toate elementele 1 – rumanisht" lang="ro" hreflang="ro" data-title="Matrice cu toate elementele 1" data-language-autonym="Română" data-language-local-name="rumanisht" 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%9C%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B0_%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%86" title="Матрица единиц – rusisht" lang="ru" hreflang="ru" data-title="Матрица единиц" data-language-autonym="Русский" data-language-local-name="rusisht" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Matrika_enic" title="Matrika enic – sllovenisht" lang="sl" hreflang="sl" data-title="Matrika enic" data-language-autonym="Slovenščina" data-language-local-name="sllovenisht" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%92%E0%AE%A9%E0%AF%8D%E0%AE%B1%E0%AF%81%E0%AE%95%E0%AE%B3%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%85%E0%AE%A3%E0%AE%BF" title="ஒன்றுகளின் அணி – tamilisht" lang="ta" hreflang="ta" data-title="ஒன்றுகளின் அணி" data-language-autonym="தமிழ்" data-language-local-name="tamilisht" 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%B9%80%E0%B8%A1%E0%B8%97%E0%B8%A3%E0%B8%B4%E0%B8%81%E0%B8%8B%E0%B9%8C%E0%B8%AB%E0%B8%99%E0%B8%B6%E0%B9%88%E0%B8%87" title="เมทริกซ์หนึ่ง – tajlandisht" lang="th" hreflang="th" data-title="เมทริกซ์หนึ่ง" data-language-autonym="ไทย" data-language-local-name="tajlandisht" 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/Birler_matrisi" title="Birler matrisi – turqisht" lang="tr" hreflang="tr" data-title="Birler matrisi" data-language-autonym="Türkçe" data-language-local-name="turqisht" 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%9C%D0%B0%D1%82%D1%80%D0%B8%D1%86%D1%8F_%D0%BE%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D1%8C" title="Матриця одиниць – ukrainisht" lang="uk" hreflang="uk" data-title="Матриця одиниць" data-language-autonym="Українська" data-language-local-name="ukrainisht" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%80%E7%9F%A9%E9%99%A3" title="一矩陣 – kinezisht" lang="zh" hreflang="zh" data-title="一矩陣" data-language-autonym="中文" data-language-local-name="kinezisht" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit 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Please update your browser bookmarks and please use the default browser print function instead.</div></div><div class="mw-content-ltr mw-parser-output" lang="sq" dir="ltr"><p>Në <a href="/wiki/Matematika" title="Matematika">matematikë</a>, një <b>matricë e njësheve</b> është një <a href="/wiki/Matrica" title="Matrica">matricë</a> ku çdo element është i barabartë me <a href="/wiki/1_(num%C3%ABr)" title="1 (numër)">një</a> . <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Shembuj të shënimeve standarde janë dhënë më poshtë: </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 J_{2}={\begin{pmatrix}1&1\\1&1\end{pmatrix}};\quad J_{3}={\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}};\quad J_{2,5}={\begin{pmatrix}1&1&1&1&1\\1&1&1&1&1\end{pmatrix}};\quad J_{1,2}={\begin{pmatrix}1&1\end{pmatrix}}.\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>;</mo> <mspace width="1em" /> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>;</mo> <mspace width="1em" /> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>,</mo> <mn>5</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>;</mo> <mspace width="1em" /> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>.</mo> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{2}={\begin{pmatrix}1&1\\1&1\end{pmatrix}};\quad J_{3}={\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}};\quad J_{2,5}={\begin{pmatrix}1&1&1&1&1\\1&1&1&1&1\end{pmatrix}};\quad J_{1,2}={\begin{pmatrix}1&1\end{pmatrix}}.\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3bdab17eb6a11d3d2344861285f5f15ec919608" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:85.624ex; height:9.176ex;" alt="{\displaystyle J_{2}={\begin{pmatrix}1&1\\1&1\end{pmatrix}};\quad J_{3}={\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}};\quad J_{2,5}={\begin{pmatrix}1&1&1&1&1\\1&1&1&1&1\end{pmatrix}};\quad J_{1,2}={\begin{pmatrix}1&1\end{pmatrix}}.\quad }"></span></dd></dl> <p>Disa burime e quajnë matricën me të gjitha njësha <b>matrica njësi</b>, por ky term mund t'i referohet gjithashtu matricës së identitetit, një lloj tjetër matrice. </p> <div class="mw-heading mw-heading2"><h2 id="Vetitë"><span id="Vetit.C3.AB"></span>Vetitë</h2></div> <p>Për një matricë njëshesh <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 n\times n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>×</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\times n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59d2b4cb72e304526cf5b5887147729ea259da78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.63ex; height:1.676ex;" alt="{\displaystyle n\times n}"></span> të shënuar me <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 {\ce {J}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>J</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {J}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65ce15065ccc4d26725a95db964bb39c8f39f68c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.195ex; height:2.176ex;" alt="{\displaystyle {\ce {J}}}"></span>, vlejnë vetitë e mëposhtme: </p> <ul><li>Gjurma e <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> është e barabartë me <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>, <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> dhe <a href="/wiki/Determinanti" title="Determinanti">përcaktori</a> është e barabartë me 0 për <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 n\geq 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6bf67f9d06ca3af619657f8d20ee1322da77174" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.656ex; height:2.343ex;" alt="{\displaystyle n\geq 2}"></span>, por është e barabartë me 1 nëse <i>n</i> = 1. <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></li> <li><a href="/w/index.php?title=Polinom_karakteristik&action=edit&redlink=1" class="new" title="Polinom karakteristik (nuk është shkruar akoma)">Polinomi karakteristik</a> 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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> është <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-n)x^{n-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>n</mi> <mo stretchy="false">)</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x-n)x^{n-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6599421f1ca21b288b93849bdb4d2ce5f0655704" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.023ex; height:3.176ex;" alt="{\displaystyle (x-n)x^{n-1}}"></span> .</li> <li>Polinomi minimal 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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> është <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^{2}-nx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>n</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}-nx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4514288a32ab102be9de01ab8a5d9e25571f1f2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.949ex; height:2.843ex;" alt="{\displaystyle x^{2}-nx}"></span> .</li> <li>Rangu 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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> është 1 dhe eigenvlerat janë <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> me shumësi 1 dhe 0 me shumësi <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 n-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd0b0f32b28f51962943ee9ede4fb34198a2521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-1}"></span> . <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J^{k}=n^{k-1}J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J^{k}=n^{k-1}J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e82137d1a68be7482ce8ec1db7d4c5d7f04ee912" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.768ex; height:2.676ex;" alt="{\displaystyle J^{k}=n^{k-1}J}"></span> për <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 k=1,2,\ldots .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=1,2,\ldots .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d56107db347f04e35db22f00cc9038a1eca27370" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.46ex; height:2.509ex;" alt="{\displaystyle k=1,2,\ldots .}"></span> <sup id="cite_ref-timm_5-0" class="reference"><a href="#cite_note-timm-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> është elementi neutral i produktit Hadamard . <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul> <p>Kur <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 J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/359e4f407b49910e02c27c2f52e87a36cd74c053" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.176ex;" alt="{\displaystyle J}"></span> konsiderohet si një matricë mbi <a href="/wiki/Numrat_real%C3%AB" title="Numrat realë">numrat realë</a>, qëndrojnë vetitë e mëposhtme shtesë: </p> <ul><li><i>J</i> është matricë gjysëm e përcaktuar pozitive .</li> <li>Matrica <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 {\tfrac {1}{n}}J}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mstyle> </mrow> <mi>J</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{n}}J}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8508a124ee834914c8639399349b163f6fc496b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.294ex; height:3.343ex;" alt="{\displaystyle {\tfrac {1}{n}}J}"></span> është idempotente . <sup id="cite_ref-timm_5-1" class="reference"><a href="#cite_note-timm-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>Eksponenciali i matricës së <i>J</i> është <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{J}=I+{\frac {e^{n}-1}{n}}J.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>J</mi> </mrow> </msup> <mo>=</mo> <mi>I</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </mrow> <mi>J</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{J}=I+{\frac {e^{n}-1}{n}}J.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b482b4b13d34f46baac0207b3d80492337e6f55f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.726ex; height:5.176ex;" alt="{\displaystyle e^{J}=I+{\frac {e^{n}-1}{n}}J.}"></span></li></ul> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r2706204">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFHornJohnson2012" class="citation cs2">Horn, Roger A.; <a href="/w/index.php?title=Charles_Royal_Johnson&action=edit&redlink=1" class="new" title="Charles Royal Johnson (nuk është shkruar akoma)">Johnson, Charles R.</a> (2012), "0.2.8 The all-ones matrix and vector", <a rel="nofollow" class="external text" href="https://books.google.com/books?id=5I5AYeeh0JUC&pg=PA8"><i>Matrix Analysis</i></a>, Cambridge University Press, fq. 8, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/9780521839402" title="Speciale:BurimetELibrave/9780521839402"><bdi>9780521839402</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=0.2.8+The+all-ones+matrix+and+vector&rft.btitle=Matrix+Analysis&rft.pages=8&rft.pub=Cambridge+University+Press&rft.date=2012&rft.isbn=9780521839402&rft.aulast=Horn&rft.aufirst=Roger+A.&rft.au=Johnson%2C+Charles+R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D5I5AYeeh0JUC%26pg%3DPA8&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AMatrica+e+nj%C3%ABsheve" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFStanley2013" class="citation cs2"><a href="/w/index.php?title=Richard_P._Stanley&action=edit&redlink=1" class="new" title="Richard P. Stanley (nuk është shkruar akoma)">Stanley, Richard P.</a> (2013), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_Tc_AAAAQBAJ&pg=PA4"><i>Algebraic Combinatorics: Walks, Trees, Tableaux, and More</i></a>, Springer, Lemma 1.4, p. 4, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/9781461469988" title="Speciale:BurimetELibrave/9781461469988"><bdi>9781461469988</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Algebraic+Combinatorics%3A+Walks%2C+Trees%2C+Tableaux%2C+and+More&rft.pages=Lemma+1.4%2C+p.-4&rft.pub=Springer&rft.date=2013&rft.isbn=9781461469988&rft.aulast=Stanley&rft.aufirst=Richard+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_Tc_AAAAQBAJ%26pg%3DPA4&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AMatrica+e+nj%C3%ABsheve" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> <span class="reference-text"><a href="#CITEREFStanley2013">Stanley (2013)</a>; <a href="#CITEREFHornJohnson2012">Horn & Johnson (2012)</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=5I5AYeeh0JUC&pg=PA65">p. 65</a>.</span> </li> <li id="cite_note-timm-5">^ <a href="#cite_ref-timm_5-0"><sup>a</sup></a> <a href="#cite_ref-timm_5-1"><sup>b</sup></a> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFTimm2002" class="citation cs2">Timm, Neil H. (2002), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vtiyg6fnnskC&pg=PA30"><i>Applied Multivariate Analysis</i></a>, Springer texts in statistics, Springer, fq. 30, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/9780387227719" title="Speciale:BurimetELibrave/9780387227719"><bdi>9780387227719</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Applied+Multivariate+Analysis&rft.series=Springer+texts+in+statistics&rft.pages=30&rft.pub=Springer&rft.date=2002&rft.isbn=9780387227719&rft.aulast=Timm&rft.aufirst=Neil+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dvtiyg6fnnskC%26pg%3DPA30&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AMatrica+e+nj%C3%ABsheve" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>. <span class="error mw-ext-cite-error" lang="sq" dir="ltr">Gabim referencash: Invalid <code><ref></code> tag; name "timm" defined multiple times with different content</span></span> </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFSmith2011" class="citation cs2">Smith, Jonathan D. H. (2011), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PQUAQh04lrUC&pg=PA77"><i>Introduction to Abstract Algebra</i></a>, CRC Press, fq. 77, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/9781420063721" title="Speciale:BurimetELibrave/9781420063721"><bdi>9781420063721</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Abstract+Algebra&rft.pages=77&rft.pub=CRC+Press&rft.date=2011&rft.isbn=9781420063721&rft.aulast=Smith&rft.aufirst=Jonathan+D.+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPQUAQh04lrUC%26pg%3DPA77&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AMatrica+e+nj%C3%ABsheve" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</span> </li> </ol><p><br /><span class="error mw-ext-cite-error" lang="sq" dir="ltr">Gabim referencash: Etiketat <code><ref></code> ekzistojnë për një grup të quajtur "lower-alpha", por nuk u gjet etiketa korresponduese <code><references group="lower-alpha"/></code></span></p></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Marrë nga "<a dir="ltr" href="https://sq.wikipedia.org/w/index.php?title=Matrica_e_njësheve&oldid=2585644">https://sq.wikipedia.org/w/index.php?title=Matrica_e_njësheve&oldid=2585644</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Speciale:Kategorit%C3%AB" title="Speciale:Kategoritë">Kategoria</a>: <ul><li><a href="/wiki/Kategoria:Gabime_CS1:_Mungon_parametri_i_gjuh%C3%ABs" title="Kategoria:Gabime CS1: Mungon parametri i gjuhës">Gabime CS1: Mungon parametri i gjuhës</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Kategori e fshehur: <ul><li><a href="/wiki/Kategoria:Pages_with_reference_errors" title="Kategoria:Pages with reference errors">Pages with reference errors</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Kjo faqe është redaktuar për herë te fundit më 10 shtator 2023, në orën 23:51.</li> <li id="footer-info-copyright">Të gjitha materialet që gjenden në këtë faqë janë të mbrojtura nga <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution/Share-Alike License</a>;. 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