{"id":300,"date":"2023-07-06T15:29:16","date_gmt":"2023-07-06T15:29:16","guid":{"rendered":"https:\/\/mathority.org\/pt\/matriz-involucional\/"},"modified":"2023-07-06T15:29:16","modified_gmt":"2023-07-06T15:29:16","slug":"matriz-involucional","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/matriz-involucional\/","title":{"rendered":"Matriz involucional"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea aprender\u00e1 o que \u00e9 uma matriz involutiva. Tamb\u00e9m mostramos exemplos de matrizes involutivas de dimens\u00f5es 2\u00d72, 3\u00d73 e 4\u00d74. E finalmente, voc\u00ea encontrar\u00e1 a f\u00f3rmula para uma matriz involucional.<\/p>\n<h2 class=\"wp-block-heading\"> O que \u00e9 uma matriz involucional?<\/h2>\n<p> O significado da matriz involucional \u00e9 o seguinte: <\/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\"> Defini\u00e7\u00e3o <strong>de matriz involutiva<\/strong> : Uma matriz quadrada invert\u00edvel cuja matriz inversa \u00e9 a pr\u00f3pria matriz.<\/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\"> Ouro<\/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> \u00e9 qualquer matriz 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> representa seu inverso.<\/p>\n<\/div>\n<p> Ent\u00e3o obviamente uma matriz involucional \u00e9 um <a href=\"https:\/\/mathority.org\/pt\/quando-e-uma-matriz-regular-ou-invertivel-exemplos-e-propriedades\/\">exemplo de matriz regular ou n\u00e3o degenerada<\/a> .<\/p>\n<p> Se voc\u00ea n\u00e3o sabe o que \u00e9 o inverso de uma matriz, pode ver aqui como calcular a <a href=\"https:\/\/mathority.org\/pt\/matriz-inversa\/\">matriz inversa 3&#215;3<\/a> . \u00c9 importante saber como inverter uma matriz, por\u00e9m, para isso tamb\u00e9m \u00e9 necess\u00e1rio saber como \u00e9 calculado o <a href=\"https:\/\/mathority.org\/pt\/exemplos-de-adjuntos-menores-de-matrizes-e-adjuntos-complementares-e-exercicios-resolvidos\/\">adjunto de uma matriz<\/a> .<\/p>\n<p> Mas voltando ao assunto: quando uma matriz \u00e9 involutiva, a multiplica\u00e7\u00e3o da matriz pela pr\u00f3pria matriz d\u00e1 a matriz identidade. D\u00ea uma olhada na demonstra\u00e7\u00e3o:<\/p>\n<p> Qualquer matriz multiplicada por sua inversa fornece a matriz Identidade (ou Unidade). ENT\u00c3O:<\/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 como o inverso de uma matriz involucional \u00e9 a pr\u00f3pria matriz:<\/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> Consequentemente, uma matriz involucional quadrada fornece a matriz identidade: <\/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=\"o que \u00e9 uma matriz involucional\" class=\"wp-image-3723\" width=\"68\" height=\"63\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Exemplos de matrizes involucionais<\/h2>\n<h3 class=\"estil_titol_H3 wp-block-heading\"> Exemplo de uma matriz 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=\"exemplo de uma matriz involutiva de dimens\u00e3o 2x2\" class=\"wp-image-3724\" width=\"143\" height=\"73\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Podemos verificar que se trata de uma matriz involucional calculando a segunda pot\u00eancia da matriz:<\/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> Como a matriz A ao quadrado \u00e9 a matriz identidade, a matriz A \u00e9 uma matriz involucional 2\u00d72.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo de uma matriz 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=\"exemplo de uma matriz involutiva de dimens\u00e3o 3x3\" class=\"wp-image-3725\" width=\"195\" height=\"108\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Podemos verificar que \u00e9 uma matriz involucional resolvendo o produto da matriz por si s\u00f3:<\/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> Como a matriz B ao quadrado \u00e9 a matriz identidade, a matriz B \u00e9 uma matriz involucional 3\u00d73.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo de uma matriz involutiva 4\u00d74:<\/h3>\n<p> A matriz Identidade (ou Unidade), qualquer que seja a sua dimens\u00e3o, \u00e9 por defini\u00e7\u00e3o uma matriz involucional.<\/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> Podemos verificar que \u00e9 uma matriz involucional elevando a matriz para 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> Como a matriz identidade quadrada \u00e9 a matriz identidade, a matriz identidade \u00e9 uma matriz involucional 4\u00d74.<\/p>\n<p> Obviamente a matriz identidade pode ser de qualquer dimens\u00e3o, pois \u00e9 simplesmente uma matriz diagonal com todos os 1s na diagonal principal e o resto 0. Portanto a matriz identidade ser\u00e1 sempre uma matriz involucional, qualquer que seja a sua ordem.<\/p>\n<h2 class=\"wp-block-heading\"> F\u00f3rmula de matriz involutiva<\/h2>\n<p> Uma das propriedades da matriz involucional \u00e9 que sua f\u00f3rmula pode ser conhecida. Mas a prova da f\u00f3rmula de uma matriz involucional de segunda ordem \u00e9 bastante tediosa, ent\u00e3o deixaremos voc\u00eas direto ao resultado, \u00e9 isso que realmente importa. Se voc\u00ea estiver mais interessado na demonstra\u00e7\u00e3o, poder\u00e1 v\u00ea-la explicada passo a passo abaixo nos coment\u00e1rios.<\/p>\n<p> A <strong>f\u00f3rmula para uma matriz involutiva<\/strong> de dimens\u00e3o 2 \u00d7 2 \u00e9 a seguinte: <\/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=\"f\u00f3rmula de matriz rolante\" class=\"wp-image-3726\" width=\"414\" height=\"134\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Portanto, qualquer matriz cujos valores da diagonal principal sejam opostos e cujo determinante seja -1, ser\u00e1 uma matriz involucional.<\/p>\n<p> Por\u00e9m, al\u00e9m das matrizes descritas por esta f\u00f3rmula, deve-se levar em considera\u00e7\u00e3o que <strong>a matriz identidade e seu oposto tamb\u00e9m s\u00e3o matrizes involucionais<\/strong> de ordem 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\"> Propriedades de uma matriz involutiva<\/h2>\n<p> As matrizes involucionais possuem as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> O <span style=\"color:#1976d2;\"><strong>determinante de uma matriz involucional<\/strong><\/span> \u00e9 sempre igual a -1 ou +1.<\/li>\n<\/ul>\n<ul>\n<li> Existe uma rela\u00e7\u00e3o entre matrizes involucionais e <span style=\"color:#1976d2;\"><strong>matrizes idempotentes<\/strong><\/span> <strong>:<\/strong> a matriz\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> \u00e9 involucional se e somente se a matriz<\/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> \u00e9 idempotente.<\/li>\n<\/ul>\n<ul>\n<li> Sim\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> s\u00e3o duas matrizes involucionais <span style=\"color:#1976d2;\"><strong>comutativas<\/strong><\/span> , ent\u00e3o o produto da matriz<\/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> tamb\u00e9m \u00e9 outra matriz involucional.<\/li>\n<\/ul>\n<ul>\n<li> Qualquer <span style=\"color:#1976d2;\"><strong>pot\u00eancia de uma matriz involucional<\/strong><\/span> resulta em outra matriz involucional. Em particular, uma matriz involucional elevada a um expoente \u00edmpar ser\u00e1 igual a si mesma, por outro lado se for elevada a um expoente par ser\u00e1 equivalente \u00e0 matriz Identidade.<\/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>Nesta p\u00e1gina voc\u00ea aprender\u00e1 o que \u00e9 uma matriz involutiva. Tamb\u00e9m mostramos exemplos de matrizes involutivas de dimens\u00f5es 2\u00d72, 3\u00d73 e 4\u00d74. E finalmente, voc\u00ea encontrar\u00e1 a f\u00f3rmula para uma matriz involucional. O que \u00e9 uma matriz involucional? O significado da matriz involucional \u00e9 o seguinte: Defini\u00e7\u00e3o de matriz involutiva : Uma matriz quadrada invert\u00edvel &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/matriz-involucional\/\"> <span class=\"screen-reader-text\">Matriz involucional<\/span> Leia mais &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":[36],"tags":[],"class_list":["post-300","post","type-post","status-publish","format-standard","hentry","category-matriz-inversa"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matriz involucional - Matoridade<\/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\/pt\/matriz-involucional\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriz involucional - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea aprender\u00e1 o que \u00e9 uma matriz involutiva. Tamb\u00e9m mostramos exemplos de matrizes involutivas de dimens\u00f5es 2\u00d72, 3\u00d73 e 4\u00d74. E finalmente, voc\u00ea encontrar\u00e1 a f\u00f3rmula para uma matriz involucional. O que \u00e9 uma matriz involucional? O significado da matriz involucional \u00e9 o seguinte: Defini\u00e7\u00e3o de matriz involutiva : Uma matriz quadrada invert\u00edvel &hellip; Matriz involucional Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/matriz-involucional\/\" \/>\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=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/matriz-involucional\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/matriz-involucional\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Matriz involucional\",\"datePublished\":\"2023-07-06T15:29:16+00:00\",\"dateModified\":\"2023-07-06T15:29:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/matriz-involucional\/\"},\"wordCount\":581,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Matriz inversa\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/matriz-involucional\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/matriz-involucional\/\",\"url\":\"https:\/\/mathority.org\/pt\/matriz-involucional\/\",\"name\":\"Matriz involucional - 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