{"id":4015,"date":"2026-10-14T23:27:00","date_gmt":"2026-10-14T22:27:00","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/matris-izi-hesaplama\/"},"modified":"2026-10-14T23:27:00","modified_gmt":"2026-10-14T22:27:00","slug":"matris-izi-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/matris-izi-hesaplama\/","title":{"rendered":"Matris izi hesaplama arac\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Kare Matrisin \u0130zini Hesaplay\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4015\" data-favorite-title=\"Matris izi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/matris-izi-hesaplama\/\" data-favorite-excerpt=\"2 \u00d7 2 veya 3 \u00d7 3 bir kare matrisin elemanlar\u0131n\u0131 girin ve izini \u2014 ana k\u00f6\u015fegen elemanlar\u0131n\u0131n toplam\u0131 olan a\u2081\u2081 + a\u2082\u2082 (+ a\u2083\u2083) \u2014 an\u0131nda \u00f6\u011frenin.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/matris-izi-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4015\" data-post=\"4015\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Matris boyutu<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"matris_boyutu\"><option value=\"2\">2 \u00d7 2<\/option><option value=\"3\" selected>3 \u00d7 3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-2\"><span class=\"font-semibold\">A matrisi<\/span><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">a\u2081\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-3\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">a\u2081\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-4\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-5\" hidden><label for=\"field-5\">a\u2081\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-5\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">a\u2082\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-6\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">a\u2082\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-7\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-8\" hidden><label for=\"field-8\">a\u2082\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-8\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-9\" hidden><label for=\"field-9\">a\u2083\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-9\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-10\" hidden><label for=\"field-10\">a\u2083\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-10\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-11\" hidden><label for=\"field-11\">a\u2083\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-11\" step=\"any\" value=\"9\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4015\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>\u0130z (tr A)<\/span><span class=\"result-term\">tr<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Toplanan k\u00f6\u015fegen elemanlar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4015\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Matris izi form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[\n\\operatorname{tr}(A) = \\sum_{i=1}^{n} a_{ii} = a_{11} + a_{22} + \\dots + a_{nn}\n\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(a_{ii}\\) \u2014 \\(A\\) matrisinin \\(i\\). sat\u0131r\u0131ndaki, \\(i\\). s\u00fctunundaki eleman (ana k\u00f6\u015fegenin bir eleman\u0131)<\/li>\n<li>\\(n\\) \u2014 kare matrisin boyutu (sat\u0131r say\u0131s\u0131 = s\u00fctun say\u0131s\u0131)<\/li>\n<\/ul>\n<p>Kare bir matrisin izi, ana k\u00f6\u015fegen \u00fczerindeki elemanlar\u0131n \u2014 yani sat\u0131r indeksi s\u00fctun indeksine e\u015fit olan elemanlar\u0131n \u2014 toplam\u0131d\u0131r. \u0130z yaln\u0131zca kare matrislerde tan\u0131ml\u0131d\u0131r; dikd\u00f6rtgen bir matrisin, uzunlu\u011fu ve geni\u015fli\u011fi e\u015fit olan iyi tan\u0131ml\u0131 bir ana k\u00f6\u015fegeni yoktur.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Matris izi \u2013 hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> elemanlar\u0131 1'den 9'a kadar sat\u0131r sat\u0131r s\u0131ralanan 3 \u00d7 3 matrisin izini bulun (bunlar hesaplay\u0131c\u0131n\u0131n varsay\u0131lan de\u011ferleridir).<\/p>\n<p>\\[<br \/>\nA = \\begin{pmatrix} 1 &amp; 2 &amp; 3 \\\\ 4 &amp; 5 &amp; 6 \\\\ 7 &amp; 8 &amp; 9 \\end{pmatrix}<br \/>\n\\]<\/p>\n<p>\\[<br \/>\n\\operatorname{tr}(A) = a_{11} + a_{22} + a_{33} = 1 + 5 + 9 = 15<br \/>\n\\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(\\operatorname{tr}(A) = 15\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Matris boyutu<\/strong> a\u00e7\u0131l\u0131r listesini a\u00e7\u0131n ve <strong>2 \u00d7 2<\/strong> ya da <strong>3 \u00d7 3<\/strong> se\u00e7in. Giri\u015f \u0131zgaras\u0131 otomatik olarak uyum sa\u011flar: 2 \u00d7 2 matriste \u00fc\u00e7\u00fcnc\u00fc sat\u0131r ve \u00fc\u00e7\u00fcnc\u00fc s\u00fctun gizlenir.<\/li>\n<li><strong>A matrisinin<\/strong> alanlar\u0131n\u0131 (a\u2081\u2081, a\u2081\u2082, \u2026) matrisinizin elemanlar\u0131yla sat\u0131r sat\u0131r doldurun. Her etiket konumu g\u00f6sterir: a\u2082\u2083, 2. sat\u0131r\u0131n 3. s\u00fctunudur.<\/li>\n<li>Sonucu okuyun: <strong>\u0130z (tr A)<\/strong> ana k\u00f6\u015fegen elemanlar\u0131n\u0131n toplam\u0131d\u0131r; <strong>toplanan k\u00f6\u015fegen elemanlar\u0131<\/strong> ise hangi say\u0131lar\u0131n topland\u0131\u011f\u0131n\u0131 tek tek g\u00f6sterir.<\/li>\n<li>Herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 an\u0131nda g\u00fcncellenir \u2014 basman\u0131z gereken bir d\u00fc\u011fme yoktur.<\/li>\n<\/ol>\n<h2>Matrisin izi nedir?<\/h2>\n<p>\u0130z, bir kare matrise ba\u011fl\u0131 say\u0131lar\u0131n en basit ama en \u00f6nemlilerinden biridir. K\u00fc\u00e7\u00fck bir \u00f6zet gibi g\u00f6r\u00fcnse de derin yap\u0131sal bilgi ta\u015f\u0131r: iz, matrisin \u00f6zde\u011ferlerinin \u00e7okluklar\u0131yla birlikte toplam\u0131na e\u015fittir. \u00d6zde\u011ferleri \\(\\lambda_1\\) ve \\(\\lambda_2\\) olan 2 \u00d7 2 bir \\(A\\) matrisi i\u00e7in daima \\(\\operatorname{tr}(A) = \\lambda_1 + \\lambda_2\\) olur; determinant ise \\(\\det(A) = \\lambda_1 \\lambda_2\\) de\u011ferini verir. Bu y\u00fczden iz, karakteristik polinomda, dinamik sistemlerin kararl\u0131l\u0131k analizinde ve kuantum mekani\u011finde \u2014 bir operat\u00f6r\u00fcn izi bir g\u00f6zlenebilirin beklenen de\u011ferini verir \u2014 s\u00fcrekli kar\u015f\u0131m\u0131za \u00e7\u0131kar.<\/p>\n<p>\u0130z ayr\u0131ca matris ispatlar\u0131nda ve hesaplamalarda b\u00fcy\u00fck kolayl\u0131k sa\u011flayan cebirsel \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li><strong>Do\u011frusall\u0131k:<\/strong> \\(\\operatorname{tr}(A + B) = \\operatorname{tr}(A) + \\operatorname{tr}(B)\\) ve \\(\\operatorname{tr}(cA) = c\\,\\operatorname{tr}(A)\\).<\/li>\n<li><strong>D\u00f6ng\u00fcsel \u00f6zellik:<\/strong> \\(\\operatorname{tr}(ABC) = \\operatorname{tr}(BCA) = \\operatorname{tr}(CAB)\\); bu sayede \\(AB \\neq BA\\) olsa bile \\(\\operatorname{tr}(AB) = \\operatorname{tr}(BA)\\) olur.<\/li>\n<li><strong>Benzerlik alt\u0131nda de\u011fi\u015fmezlik:<\/strong> \\(B = P^{-1}AP\\) ise \\(\\operatorname{tr}(B) = \\operatorname{tr}(A)\\). \u0130z hangi tabanda al\u0131n\u0131rsa al\u0131ns\u0131n ayn\u0131d\u0131r.<\/li>\n<\/ul>\n<p>Geometrik a\u00e7\u0131dan, matris bir do\u011frusal d\u00f6n\u00fc\u015f\u00fcm\u00fc temsil ediyorsa iz, d\u00f6n\u00fc\u015f\u00fcm\u00fcn hacmi k\u00f6\u015fegen y\u00f6n\u00fcnde yerel olarak nas\u0131l \u00f6l\u00e7ekledi\u011fini \u00f6l\u00e7er: pozitif iz germeyi, negatif iz s\u0131k\u0131\u015ft\u0131rmay\u0131 g\u00f6sterir; s\u0131f\u0131r iz ise k\u00f6\u015fegen katk\u0131lar\u0131n birbirini yok etti\u011fi anlam\u0131na gelir. Graf teorisinde \\(A^k\\) matrisinin izi, \\(A\\) matrisinin tan\u0131mlad\u0131\u011f\u0131 grafte uzunlu\u011fu \\(k\\) olan kapal\u0131 yollar\u0131n say\u0131s\u0131n\u0131 verir.<\/p>\n<h2>Varsay\u0131mlar ve pratik ipu\u00e7lar\u0131<\/h2>\n<p>Bu hesaplay\u0131c\u0131 2 \u00d7 2 ve 3 \u00d7 3 matrislerle \u00e7al\u0131\u015f\u0131r ve eleman olarak negatif ve ondal\u0131kl\u0131 de\u011ferler dahil herhangi bir ger\u00e7ek say\u0131y\u0131 kabul eder. Girdi\u011finiz k\u00f6\u015fegen d\u0131\u015f\u0131 elemanlar sonucu etkilemez \u2014 iz yaln\u0131zca ana k\u00f6\u015fegene ba\u011fl\u0131d\u0131r \u2014 ama matrisin tam olarak tan\u0131mlanmas\u0131 i\u00e7in bu alanlar\u0131 da doldurman\u0131z gerekir.<\/p>\n<p>Sonucunuzu yorumlarken \u015funlara dikkat edin:<\/p>\n<ul>\n<li><strong>Yaln\u0131zca kare matrisler.<\/strong> Verileriniz dikd\u00f6rtgen bir matris (\u00f6rne\u011fin 2 \u00d7 3) olu\u015fturuyorsa iz tan\u0131ml\u0131 de\u011fildir. Verilerinizin ger\u00e7ekte neyi temsil etti\u011fini g\u00f6zden ge\u00e7irin ya da matrisi kare bir bi\u00e7ime d\u00f6n\u00fc\u015ft\u00fcr\u00fcn.<\/li>\n<li><strong>\u0130z tek bir say\u0131d\u0131r,<\/strong> matris de\u011fil. S\u0131f\u0131r iz, matrisin s\u0131f\u0131r ya da \u00f6nemsiz oldu\u011fu anlam\u0131na gelmez \u2014 s\u0131f\u0131rdan farkl\u0131 pek \u00e7ok matrisin (\u00f6rne\u011fin d\u00f6n\u00fc\u015f matrislerinin) izi s\u0131f\u0131rd\u0131r.<\/li>\n<li><strong>\u0130z ve determinant birlikte,<\/strong> \\(\\lambda^2 - \\operatorname{tr}(A)\\,\\lambda + \\det(A) = 0\\) ikinci derece denklemi arac\u0131l\u0131\u011f\u0131yla herhangi bir 2 \u00d7 2 matrisin \u00f6zde\u011ferlerini tamamen belirler. Karma\u015f\u0131k \u00f6zde\u011ferler daima e\u015flenik \u00e7iftler halinde gelir \u2014 <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/karmasik-eslenik\/\">Karma\u015f\u0131k E\u015flenik hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n \u2014 bu y\u00fczden \\(\\operatorname{tr}(A)^2 &lt; 4\\det(A)\\) olan ger\u00e7ek bir 2 \u00d7 2 matrisin \u00f6zde\u011ferleri karma\u015f\u0131kt\u0131r.<\/li>\n<\/ul>\n<p>Say\u0131 \u0131zgaralar\u0131yla ba\u015fka ba\u011flamlarda m\u0131 \u00e7al\u0131\u015f\u0131yorsunuz? K\u00f6\u015fegenler bulmacularda da \u00f6nem ta\u015f\u0131r \u2014 <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/sihirli-kare-uretici\/\">Sihirli Kare olu\u015fturucuyu<\/a> deneyin; orada her sat\u0131r, s\u00fctun ve k\u00f6\u015fegen ayn\u0131 toplama e\u015fit olmak zorundad\u0131r. Matris \u00e7al\u0131\u015fman\u0131z sizi do\u011frusal denklem sistemleri \u00e7\u00f6zmeye g\u00f6t\u00fcr\u00fcyorsa <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/yok-etme-yontemi\/\">Eleme Y\u00f6ntemi hesaplay\u0131c\u0131s\u0131<\/a> bir sonraki ad\u0131m\u0131 sizin i\u00e7in halleder.<\/p>\n<p>[\/wp_code]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>2 \u00d7 2 veya 3 \u00d7 3 bir kare matrisin elemanlar\u0131n\u0131 girin ve izini \u2014 ana k\u00f6\u015fegen elemanlar\u0131n\u0131n toplam\u0131 olan a\u2081\u2081 + a\u2082\u2082 (+ a\u2083\u2083) \u2014 an\u0131nda \u00f6\u011frenin.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[54],"class_list":["post-4015","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-matris"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4015","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4015"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4015\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}