{"id":303,"date":"2023-07-06T15:29:16","date_gmt":"2023-07-06T15:29:16","guid":{"rendered":"https:\/\/mathority.org\/it\/matrice-involutiva\/"},"modified":"2023-07-06T15:29:16","modified_gmt":"2023-07-06T15:29:16","slug":"matrice-involutiva","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/matrice-involutiva\/","title":{"rendered":"Matrice involutiva"},"content":{"rendered":"<p>In questa pagina imparerai cos&#8217;\u00e8 una matrice involutiva. Vi mostriamo anche esempi di matrici involutive di dimensioni 2\u00d72, 3\u00d73 e 4\u00d74. E infine troverai la formula per una matrice involutiva.<\/p>\n<h2 class=\"wp-block-heading\"> Cos&#8217;\u00e8 una matrice involutiva?<\/h2>\n<p> Il significato della matrice involutiva \u00e8 il seguente: <\/p>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p style=\"text-align:left\"> Definizione <strong>di matrice involutiva<\/strong> : matrice quadrata invertibile la cui matrice inversa \u00e8 la matrice stessa.<\/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-8711e2a47f90783a00a3bdd571df2175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{-1} = A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Oro<\/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-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e8 una matrice qualsiasi e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2b32875906f7ed9c10ffd1b09a6ed5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<p> rappresenta il suo inverso.<\/p>\n<\/div>\n<p> Quindi ovviamente una matrice involutiva \u00e8 un <a href=\"https:\/\/mathority.org\/it\/quando-e-una-matrice-regolare-o-invertibile-esempi-e-proprieta\/\">esempio di matrice regolare o non degenere<\/a> .<\/p>\n<p> Se non sai cos&#8217;\u00e8 l&#8217;inversa di una matrice, puoi vedere qui come calcolare la <a href=\"https:\/\/mathority.org\/it\/matrice-inversa\/\">matrice inversa 3&#215;3<\/a> . \u00c8 importante sapere come invertire una matrice, tuttavia per questo \u00e8 necessario anche sapere come si calcola l&#8217; <a href=\"https:\/\/mathority.org\/it\/esempi-di-aggiunti-minori-e-complementari-di-matrice-ed-esercizi-risolti\/\">aggiunto di una matrice<\/a> .<\/p>\n<p> Ma torniamo all&#8217;argomento: quando una matrice \u00e8 involutiva, la moltiplicazione della matrice per la matrice stessa d\u00e0 la matrice identit\u00e0. Dai un&#8217;occhiata alla demo:<\/p>\n<p> Qualsiasi matrice moltiplicata per il suo inverso d\u00e0 la matrice Identit\u00e0 (o Unit\u00e0). COS\u00cc:<\/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-2326f8acf7b6701e027cafdaae59b38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot A^{-1} = I\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> E poich\u00e9 l&#8217;inverso di una matrice involutiva \u00e8 la matrice stessa:<\/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-b8c3afa923ef022a2d25738eb843390b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot A = I\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Di conseguenza, una matrice involutiva quadrata d\u00e0 la matrice identit\u00e0: <\/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\/quest-ce-quune-matrice-involutive.webp\" alt=\"cos'\u00e8 una matrice involutiva\" class=\"wp-image-3723\" width=\"68\" height=\"63\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Esempi di matrici involutive<\/h2>\n<h3 class=\"estil_titol_H3 wp-block-heading\"> Esempio di matrice involutiva 2\u00d72: <\/h3>\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-involutive-22152-1.webp\" alt=\"esempio di matrice involutiva di dimensione 2x2\" class=\"wp-image-3724\" width=\"143\" height=\"73\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Possiamo verificare che si tratta di una matrice involutiva calcolando la seconda potenza della matrice:<\/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-314aebadfe3da501264c0eb14e1dfc2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2=\\begin{pmatrix} 2 &amp; 3 \\\\[1.1ex] -1 &amp; -2 \\end{pmatrix} \\cdot \\begin{pmatrix} 2 &amp; 3 \\\\[1.1ex] -1 &amp; -2 \\end{pmatrix}= \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"318\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Poich\u00e9 la matrice A al quadrato \u00e8 la matrice identit\u00e0, la matrice A \u00e8 una matrice involutiva 2\u00d72.<\/p>\n<h3 class=\"wp-block-heading\"> Esempio di matrice involutiva 3\u00d73: <\/h3>\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-involutive-32153-1.webp\" alt=\"esempio di matrice involutiva di dimensione 3x3\" class=\"wp-image-3725\" width=\"195\" height=\"108\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Possiamo verificare che si tratta di una matrice involutiva risolvendo da sola il prodotto della matrice:<\/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-599241f00e8a89f8b55ed2ae8cb42ddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^2=\\begin{pmatrix} 2 &amp; 1 &amp; 1 \\\\[1.1ex] -1 &amp; 0 &amp; -1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\end{pmatrix}\\cdot \\begin{pmatrix} 2 &amp; 1 &amp; 1 \\\\[1.1ex] -1 &amp; 0 &amp; -1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\end{pmatrix}= \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"430\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Poich\u00e9 la matrice B al quadrato \u00e8 la matrice identit\u00e0, la matrice B \u00e8 una matrice involutiva 3\u00d73.<\/p>\n<h3 class=\"wp-block-heading\"> Esempio di matrice involutiva 4\u00d74:<\/h3>\n<p> La matrice Identit\u00e0 (o Unit\u00e0), qualunque sia la sua dimensione, \u00e8 per definizione una matrice involutiva.<\/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-4278c2b46761d3b258eb9ba04c87bbf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I=\\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"143\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Possiamo verificare che si tratta di una matrice involutiva elevando la matrice a 2:<\/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-c3190f24d196c4b96a60ec06fe7180e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I^2=\\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}\\cdot \\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}= \\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"418\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Poich\u00e9 la matrice identit\u00e0 quadrata \u00e8 la matrice identit\u00e0, la matrice identit\u00e0 \u00e8 una matrice involutiva 4\u00d74.<\/p>\n<p> Ovviamente la matrice identit\u00e0 pu\u00f2 avere qualsiasi dimensione, poich\u00e9 \u00e8 semplicemente una matrice diagonale con tutti gli 1 sulla diagonale principale e il resto 0. Quindi la matrice identit\u00e0 sar\u00e0 sempre una matrice involutiva, qualunque sia il suo ordine.<\/p>\n<h2 class=\"wp-block-heading\"> Formula della matrice involutiva<\/h2>\n<p> Una delle propriet\u00e0 della matrice involutiva \u00e8 che la sua formula pu\u00f2 essere conosciuta. Ma la dimostrazione della formula per una matrice involutiva del secondo ordine \u00e8 piuttosto noiosa, quindi ti lasciamo direttamente al risultato, questo \u00e8 ci\u00f2 che \u00e8 veramente importante. Se sei pi\u00f9 interessato alla demo, puoi vederla spiegata passo dopo passo qui sotto nei commenti.<\/p>\n<p> La <strong>formula per una matrice involutiva<\/strong> di dimensione 2 \u00d7 2 \u00e8 la seguente: <\/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\/formule-matricielle-involutive.webp\" alt=\"formula della matrice mobile\" class=\"wp-image-3726\" width=\"414\" height=\"134\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Pertanto, qualsiasi matrice i cui valori della diagonale principale siano opposti e il cui determinante sia -1, sar\u00e0 una matrice involutiva.<\/p>\n<p> Tuttavia, oltre alle matrici descritte da questa formula, bisogna tenere conto che <strong>anche la matrice identit\u00e0 e il suo opposto sono matrici involutive<\/strong> di ordine 2:<\/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-395beb5a766a10eefa56a087e8c8d098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix} \\qquad \\begin{pmatrix} -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"182\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Propriet\u00e0 di una matrice involutiva<\/h2>\n<p> Le matrici involutive hanno le seguenti caratteristiche:<\/p>\n<ul>\n<li> Il <span style=\"color:#1976d2;\"><strong>determinante di una matrice involutiva<\/strong><\/span> \u00e8 sempre uguale a -1 o +1.<\/li>\n<\/ul>\n<ul>\n<li> Esiste una relazione tra matrici involutive e <span style=\"color:#1976d2;\"><strong>matrici idempotenti<\/strong><\/span> <strong>:<\/strong> la matrice\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e8 involutivo se e solo se la matrice<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37b99c07f3a3eb03d02d9448a923078e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Q= \\cfrac{1}{2} \\cdot (A+I)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"118\" style=\"vertical-align: -12px;\"><\/p>\n<p> \u00e8 idempotente.<\/li>\n<\/ul>\n<ul>\n<li> S\u00ec\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> sono due matrici involutive <span style=\"color:#1976d2;\"><strong>commutanti<\/strong><\/span> , quindi il prodotto di matrici<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89b2a721cf233a7e57685324f6648a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"AB\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e8 anche un&#8217;altra matrice involutiva.<\/li>\n<\/ul>\n<ul>\n<li> Qualsiasi <span style=\"color:#1976d2;\"><strong>potenza di una matrice involutiva<\/strong><\/span> si traduce in un&#8217;altra matrice involutiva. In particolare una matrice involutiva elevata ad esponente dispari sar\u00e0 uguale a se stessa, se invece \u00e8 elevata ad esponente pari sar\u00e0 equivalente alla matrice Identit\u00e0.<\/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-03f040ce22790ca420cd1614b4ee3c5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^2 = I\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\"><\/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-639e56b4e1e25d1a3743cd2768cf21b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^3 = A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In questa pagina imparerai cos&#8217;\u00e8 una matrice involutiva. Vi mostriamo anche esempi di matrici involutive di dimensioni 2\u00d72, 3\u00d73 e 4\u00d74. E infine troverai la formula per una matrice involutiva. Cos&#8217;\u00e8 una matrice involutiva? Il significato della matrice involutiva \u00e8 il seguente: Definizione di matrice involutiva : matrice quadrata invertibile la cui matrice inversa \u00e8 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/matrice-involutiva\/\"> <span class=\"screen-reader-text\">Matrice involutiva<\/span> Leggi altro &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":[31],"tags":[],"class_list":["post-303","post","type-post","status-publish","format-standard","hentry","category-matrice-inversa"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matrice involutiva - Mathority<\/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\/it\/matrice-involutiva\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matrice involutiva - Mathority\" \/>\n<meta property=\"og:description\" content=\"In questa pagina imparerai cos&#8217;\u00e8 una matrice involutiva. Vi mostriamo anche esempi di matrici involutive di dimensioni 2\u00d72, 3\u00d73 e 4\u00d74. E infine troverai la formula per una matrice involutiva. Cos&#8217;\u00e8 una matrice involutiva? Il significato della matrice involutiva \u00e8 il seguente: Definizione di matrice involutiva : matrice quadrata invertibile la cui matrice inversa \u00e8 &hellip; Matrice involutiva Leggi altro &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/it\/matrice-involutiva\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T15:29:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8711e2a47f90783a00a3bdd571df2175_l3.png\" \/>\n<meta name=\"author\" content=\"Squadra di Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Scritto da\" \/>\n\t<meta name=\"twitter:data1\" content=\"Squadra di Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo di lettura stimato\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minuti\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/it\/matrice-involutiva\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/it\/matrice-involutiva\/\"},\"author\":{\"name\":\"Squadra di Mathority\",\"@id\":\"https:\/\/mathority.org\/it\/#\/schema\/person\/8d6f69ffbe48aea8b43675a9a3ddb9c8\"},\"headline\":\"Matrice involutiva\",\"datePublished\":\"2023-07-06T15:29:16+00:00\",\"dateModified\":\"2023-07-06T15:29:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/it\/matrice-involutiva\/\"},\"wordCount\":540,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/it\/#organization\"},\"articleSection\":[\"Matrice inversa\"],\"inLanguage\":\"it-IT\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/it\/matrice-involutiva\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/it\/matrice-involutiva\/\",\"url\":\"https:\/\/mathority.org\/it\/matrice-involutiva\/\",\"name\":\"Matrice involutiva - 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