{"id":313,"date":"2023-07-06T12:10:47","date_gmt":"2023-07-06T12:10:47","guid":{"rendered":"https:\/\/mathority.org\/de\/skalarmatrix\/"},"modified":"2023-07-06T12:10:47","modified_gmt":"2023-07-06T12:10:47","slug":"skalarmatrix","status":"publish","type":"post","link":"https:\/\/mathority.org\/de\/skalarmatrix\/","title":{"rendered":"Skalare matrix"},"content":{"rendered":"<p>Auf dieser Seite finden Sie, was eine Skalarmatrix ist, und einige Beispiele f\u00fcr Skalarmatrizen, damit es perfekt verstanden wird. Dar\u00fcber hinaus k\u00f6nnen Sie alle Eigenschaften von Skalarmatrizen und die Vorteile der Durchf\u00fchrung von Operationen mit ihnen erkennen. Abschlie\u00dfend erkl\u00e4ren wir, wie man die Determinante einer Skalarmatrix berechnet und wie man diese Art von Matrix invertiert.<\/p>\n<h2 class=\"wp-block-heading\"> Was ist eine Skalarmatrix?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> Eine <strong>Skalarmatrix<\/strong> ist eine <a href=\"https:\/\/mathority.org\/de\/diagonale-matrix\/\"><span style=\"text-decoration: underline;\">Diagonalmatrix<\/span><\/a> , bei der alle Werte auf der Hauptdiagonale gleich sind.<\/p>\n<p> Dies ist die Definition einer Skalarmatrix, aber ich bin sicher, dass man sie anhand von Beispielen besser verstehen kann: \ud83d\ude09<\/p>\n<h2 class=\"wp-block-heading\"> Beispiele f\u00fcr Skalar-Arrays<\/h2>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Beispiel einer Skalarmatrix der Ordnung 2\u00d72<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-22152-1.webp\" alt=\"Beispiel einer Skalarmatrix der Dimension 2x2\" class=\"wp-image-1910\" width=\"80\" height=\"80\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Beispiel einer 3\u00d73-Skalarmatrix<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-3-dimensionnelle-3-1.webp\" alt=\"Beispiel einer Skalarmatrix der Dimension 3x3\" class=\"wp-image-1911\" width=\"116\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Beispiel einer Skalarmatrix der Gr\u00f6\u00dfe 4\u00d74<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-42154-1.webp\" alt=\"Beispiel einer Skalarmatrix der Dimension 4x4\" class=\"wp-image-1912\" width=\"218\" height=\"146\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Eigenschaften von Skalarmatrizen<\/h2>\n<p> Die Skalarmatrix ist auch eine Diagonalmatrix, Sie werden also sehen, dass sie viele Merkmale dieser Matrixklasse erbt:<\/p>\n<ul>\n<li> Alle Skalarmatrizen sind auch <a href=\"https:\/\/mathority.org\/de\/beispiele-und-eigenschaften-symmetrischer-matrizen\/\">symmetrische Matrizen<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> Eine Skalarmatrix ist sowohl eine <a href=\"https:\/\/mathority.org\/de\/obere-untere-dreiecksmatrix\/\">obere Dreiecksmatrix als auch eine untere Dreiecksmatrix<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> Die <a href=\"https:\/\/mathority.org\/de\">Identit\u00e4tsmatrix<\/a> ist eine Skalarmatrix.<\/li>\n<\/ul>\n<ul>\n<li> Jede Skalarmatrix kann aus dem Produkt einer Identit\u00e4tsmatrix und einer Skalarzahl erhalten werden.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b77f7d177c2769b0847de258adfd1386_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4 \\cdot \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Die <a href=\"https:\/\/mathority.org\/de\/nullmatrix-null\/\">Nullmatrix<\/a> ist ebenfalls eine Skalarmatrix.<\/li>\n<\/ul>\n<ul>\n<li> Die Eigenwerte (oder Eigenwerte) einer Skalarmatrix sind die Elemente ihrer Hauptdiagonale. Daher sind ihre Eigenwerte immer gleich und werden so oft wiederholt, wie die Dimension der Matrix.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2513b8d4aeb6d932d9870934102a1637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 8 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 8 \\end{pmatrix} \\longrightarrow \\ \\lambda = 8 \\ ; \\ \\lambda = 8 \\ ; \\ \\lambda = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"298\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Der Adjungierte einer Skalarmatrix ist eine andere Skalarmatrix. Dar\u00fcber hinaus sind die Werte der Hauptdiagonalen der angeh\u00e4ngten Matrix immer diejenigen der urspr\u00fcnglichen Matrix, erh\u00f6ht <em>auf die Matrixordnung \u2013 1<\/em> .<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f7e94cc5a528abace04016dc263c8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5 \\end{pmatrix} \\longrightarrow \\text{Adj}(A)=\\begin{pmatrix} 5^{3-1} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5^{3-1} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5^{3-1} \\end{pmatrix}= \\begin{pmatrix} 25 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 25 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 25 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Operationen mit Skalarmatrizen<\/h2>\n<p> Einer der Gr\u00fcnde, warum Skalarmatrizen in der linearen Algebra so h\u00e4ufig verwendet werden, ist die einfache Durchf\u00fchrung von Berechnungen. Deshalb sind sie in der Mathematik so wichtig.<\/p>\n<p> Sehen wir uns also an, warum es so einfach ist, Berechnungen mit dieser Art von quadratischer Matrix durchzuf\u00fchren:<\/p>\n<h3 class=\"wp-block-heading\"> Addition und Subtraktion von Skalarmatrizen<\/h3>\n<p> Das Addieren (und Subtrahieren) zweier Skalarmatrizen ist sehr einfach: Addieren (oder subtrahieren) Sie einfach die Zahlen auf den Hauptdiagonalen. Zum Beispiel:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-761de4b4c9bdbbc835b366b21d8cfc2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix} +\\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 7&amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"306\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Skalarmatrixmultiplikation<\/h3>\n<p> Um eine Multiplikation oder ein Matrixprodukt zwischen zwei Skalarmatrizen zu l\u00f6sen, multiplizieren Sie \u00e4hnlich wie bei der Addition und Subtraktion einfach die Elemente der Diagonalen zwischen ihnen. Zum Beispiel:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d30acbf9c6ad31625f8253549e659b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\cdot\\begin{pmatrix} 6 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 6 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix} = \\begin{pmatrix} 12 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 12 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 12 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Leistung skalarer Matrizen<\/h3>\n<p> Auch die Berechnung der Potenz einer Skalarmatrix ist sehr einfach: Man muss jedes Element der Diagonale auf den Exponenten erh\u00f6hen. Zum Beispiel:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle\\left. \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix}\\right.^4=\\begin{pmatrix} 2^ 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2^\n\n*** Error message:\nMissing $ inserted.\nleading text: \\displaystyle\nMissing { inserted.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\right. inserted.\nleading text: \\end{document}\n\n<\/pre>\n<p> &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2^4 \\end{pmatrix}= \\begin{pmatrix} 16 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 16 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 16 \\end{pmatrix}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca97d1162704371c21b308778890f436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<div class=&quot;adsb30&quot; style=&quot; margin:px; text-align:&quot;><\/div>\n<h2 class=&quot;wp-block-heading&quot;> D\u00e9terminant d&#8217;une matrice scalaire<\/h2>\n<p> Calculer le <strong>d\u00e9terminant d&#8217;une matrice scalaire<\/strong> revient \u00e0 r\u00e9soudre le d\u00e9terminant d&#8217;une matrice diagonale : le r\u00e9sultat est le produit des \u00e9l\u00e9ments sur la diagonale principale.&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;106&#8243; width=&#8220;582&#8243; style=&#8220;vertical-align: -4px;&#8220;><\/p>\n<p> \\displaystyle \\text{det}(A)= \\prod_{i =1}^n a_i<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b3ddf4b77e65a9bd0387f51b7bcaa40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Regardez l'exercice r\u00e9solu suivant dans lequel on trouve le d\u00e9terminant d'une matrice scalaire en multipliant les \u00e9l\u00e9ments de sa diagonale principale :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1099\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{vmatrix} = 7 \\cdot 7 \\cdot 7 = \\bm {343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-773692a573846f155d4c92f1e9075001_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" En fait, puisque tous les \u00e9l\u00e9ments de la diagonale principale d'une matrice scalaire sont toujours \u00e9gaux, pour trouver le r\u00e9sultat du d\u00e9terminant, il suffit d'augmenter le num\u00e9ro de la diagonale principale du nombre de fois qu'elle est r\u00e9p\u00e9t\u00e9e. Par cons\u00e9quent, l'exercice pr\u00e9c\u00e9dent peut \u00e9galement \u00eatre r\u00e9solu de la mani\u00e8re suivante :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"2411\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{vmatrix} = 7^3= \\bm{343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d24f9aa91fc9fe8ed74f705f83be3b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D\u00e9montrer ce th\u00e9or\u00e8me est tr\u00e8s simple : il suffit de calculer le d\u00e9terminant d'une matrice scalaire par blocs (ou cofacteurs). Vous trouverez ci-dessous la <strong>d\u00e9monstration<\/strong> de la formule utilisant une matrice scalaire g\u00e9n\u00e9rique :&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;62&#8243; width=&#8220;1060&#8243; style=&#8220;vertical-align: -4px;&#8220;><\/p>\n<p> \\begin{aligned} \\begin{vmatrix} a &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; a &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; a \\end{vmatrix}&amp; = a \\cdot \\begin{ vmatrix} a &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} \u2013 0 \\cdot \\begin{vmatrix} 0 &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} + 0 \\cdot \\ begin{vmatrix} 0 &amp; a \\\\[1.1ex] 0 &amp; 0 \\end{vmatrix} \\\\[2ex] &amp; =a \\cdot (a\\cdot a) \u2013 0 \\cdot 0 + 0 \\cdot 0 \\\\[ 2ex] &amp; = a \\cdot a \\cdot a \\\\[2ex] &amp; = a^3 \\end{aligned}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc127c7827a5f62c565b8ada378986a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Dans ce cas \u00e7a donne\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"149\" style=\"vertical-align: -1px;\"><\/p>\n<p> a^3<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49f5afdd3e1e9918f5323139662a2138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"car la matrice est d'ordre 3, mais il faut toujours l'\u00e9lever \u00e0 l'ordre de la matrice. \n\n<div class=&quot;adsb30&quot; style=&quot; margin:12px; text-align:center&quot;>\n<div id=&quot;ezoic-pub-ad-placeholder-118&quot;><\/div>\n<\/div>\n<h2 class=&quot;wp-block-heading&quot;> Inverser une matrice scalaire<\/h2>\n<p> Une matrice scalaire <strong>est inversible si, et seulement si, tous les \u00e9l\u00e9ments de la diagonale principale sont diff\u00e9rents de 0<\/strong> . Dans ce cas on dit que la matrice scalaire est une matrice r\u00e9guli\u00e8re. De plus, l&#8217;inverse d&#8217;une matrice scalaire sera toujours une autre matrice scalaire avec les <strong>inverses<\/strong> de la diagonale principale :&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;174&#8243; width=&#8220;1250&#8243; style=&#8220;vertical-align: -5px;&#8220;><\/p>\n<p> \\displaystyle A= \\begin{pmatrix} 9 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 9 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 9 \\end{pmatrix} \\ \\longrightarrow \\ A^{-1 }=\\begin{pmatrix} \\frac{1}{9} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; \\frac{1}{9} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; \\frac{ 1}{9} \\end{pmatrix}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eaf19f57b0cbab7f60c5c1dc0ec45eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D'autre part, de la caract\u00e9ristique pr\u00e9c\u00e9dente, on peut d\u00e9duire que le d\u00e9terminant d'une matrice scalaire invers\u00e9e est le r\u00e9sultat de la multiplication des inverses de la diagonale principale : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1373\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle B= \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\displaystyle\\left| B^{-1}\\right|=\\cfrac{1}{2} \\cdot \\cfrac{1}{2} \\cdot \\cfrac{1}{2}=\\cfrac{1}{8} = $0,125<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Auf dieser Seite finden Sie, was eine Skalarmatrix ist, und einige Beispiele f\u00fcr Skalarmatrizen, damit es perfekt verstanden wird. Dar\u00fcber hinaus k\u00f6nnen Sie alle Eigenschaften von Skalarmatrizen und die Vorteile der Durchf\u00fchrung von Operationen mit ihnen erkennen. Abschlie\u00dfend erkl\u00e4ren wir, wie man die Determinante einer Skalarmatrix berechnet und wie man diese Art von Matrix invertiert. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/de\/skalarmatrix\/\"> <span class=\"screen-reader-text\">Skalare matrix<\/span> Weiterlesen &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[32],"tags":[],"class_list":["post-313","post","type-post","status-publish","format-standard","hentry","category-arten-von-tabellen"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Skalarmatrix - Mathematik<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/de\/skalarmatrix\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Skalarmatrix - Mathematik\" \/>\n<meta property=\"og:description\" content=\"Auf dieser Seite finden Sie, was eine Skalarmatrix ist, und einige Beispiele f\u00fcr Skalarmatrizen, damit es perfekt verstanden wird. Dar\u00fcber hinaus k\u00f6nnen Sie alle Eigenschaften von Skalarmatrizen und die Vorteile der Durchf\u00fchrung von Operationen mit ihnen erkennen. 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