{"id":664270,"date":"2023-07-10T10:35:44","date_gmt":"2023-07-10T05:05:44","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=664270"},"modified":"2025-05-15T14:49:03","modified_gmt":"2025-05-15T09:19:03","slug":"symmetric-and-skew-symmetric-matrix-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/","title":{"rendered":"Symmetric and skew-symmetric matrix: examples and properties"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Symmetric_matrix\" title=\"Symmetric matrix\">Symmetric matrix<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Transpose_of_matrices\" title=\"Transpose of matrices\">Transpose of matrices<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Skew-Symmetric_Matrix\" title=\"Skew-Symmetric Matrix\">Skew-Symmetric Matrix<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Properties_of_Symmetric_and_skew-symmetric_matrices\" title=\"Properties of Symmetric and skew-symmetric matrices\">Properties of Symmetric and skew-symmetric matrices<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#What_is_the_difference_between_a_symmetric_matrix_and_a_skew-symmetric_matrix\" title=\"What is the difference between a symmetric matrix and a skew-symmetric matrix?\">What is the difference between a symmetric matrix and a skew-symmetric matrix?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#FAQs_on_Symmetric_and_Skew-symmetric_Matrix\" title=\"FAQs on Symmetric and Skew-symmetric Matrix\">FAQs on Symmetric and Skew-symmetric Matrix<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Can_a_matrix_be_both_symmetric_and_skew-symmetric\" title=\"Can a matrix be both symmetric and skew-symmetric?\">Can a matrix be both symmetric and skew-symmetric?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Are_symmetric_and_skew-symmetric_matrices_always_square_matrices\" title=\"Are symmetric and skew-symmetric matrices always square matrices?\">Are symmetric and skew-symmetric matrices always square matrices?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Are_the_eigenvalues_of_a_symmetric_matrix_real\" title=\"Are the eigenvalues of a symmetric matrix real?\">Are the eigenvalues of a symmetric matrix real?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#What_is_the_relationship_between_the_eigenvectors_of_a_symmetric_matrix\" title=\"What is the relationship between the eigenvectors of a symmetric matrix?\">What is the relationship between the eigenvectors of a symmetric matrix?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Can_a_matrix_be_both_symmetric_and_diagonal\" title=\"Can a matrix be both symmetric and diagonal?\">Can a matrix be both symmetric and diagonal?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#Can_a_matrix_be_both_skew-symmetric_and_diagonal\" title=\"Can a matrix be both skew-symmetric and diagonal?\">Can a matrix be both skew-symmetric and diagonal?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/symmetric-and-skew-symmetric-matrix\/#How_can_we_determine_if_a_matrix_is_symmetric_or_skew-symmetric\" title=\"How can we determine if a matrix is symmetric or skew-symmetric?\">How can we determine if a matrix is symmetric or skew-symmetric?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Symmetric_matrix\"><\/span>Symmetric matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Definition of a symmetric matrix: A square matrix A = [a<sub>ij<\/sub>] is called a symmetric matrix if a<sub>ij<\/sub> = a<sub>ij<\/sub>, for all i,j values<\/p>\n<p><strong>Example of the symmetric matrix:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-664271 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Symmetric-matrix-1.png\" alt=\"Symmetric matrix\" width=\"112\" height=\"111\" \/><\/p>\n<p>is an example of a symmetric matrix<\/p>\n<p>Note: Matrix A is symmetric if A\u2019 = A (where A\u2019 is the transpose of the matrix)<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Transpose_of_matrices\"><\/span>Transpose of matrices<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>To understand if a matrix is a symmetric matrix, it is very important to know about the transpose of a matrix and how to find the transpose of a matrix.<br \/>\nIf the rows and columns of an m\u00d7n matrix are interchanged to get an n \u00d7 m matrix, the new matrix obtained is called the transpose of the given matrix.<\/p>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/topics\/maths-topics\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 80px;\" type=\"button\">Maths Topics<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 80px;\" type=\"button\">Types of Matrices<\/button><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Skew-Symmetric_Matrix\"><\/span>Skew-Symmetric Matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Definition of Skew-symmetric matrix:<\/strong> A square matrix A = [aij] is a skew-symmetric matrix if aij = -aji, for all values of i,j.<\/p>\n<p>If we put i=j, then,<br \/>\na<sub>ii<\/sub> = -a<sub>ii<\/sub><br \/>\n\u21d2 2a<sub>ii<\/sub> = 0<br \/>\n\u21d2 a<sub>ii<\/sub> = 0<\/p>\n<p>Thus, <strong>in a skew-symmetric matrix, all diagonal elements are zero.<\/strong><\/p>\n<p><strong>Example of a Skew-symmetric matrix:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-664274\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Skew-Symmetric-Matrix-3.png\" alt=\"\" width=\"204\" height=\"118\" \/><\/p>\n<p>is an example of skew-symmetric matrices.<\/p>\n<p><strong>Note:<\/strong> A square matrix A is skew-symmetric if A\u2019 = -A.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Properties_of_Symmetric_and_skew-symmetric_matrices\"><\/span><strong>Properties of Symmetric and skew-symmetric matrices<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li>Every square Matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.<\/li>\n<li>If A is a symmetric Matrix, then A<sup>n<\/sup>, n belonging to the Natural number, will be symmetric.<\/li>\n<li>A is skew-symmetric, then A<sup>n<\/sup>, n N will be symmetric if n is even, and A<sup>n<\/sup> will be skew-symmetric if n is odd.<\/li>\n<li>Null Matrix is always symmetric and skew-symmetric.<\/li>\n<li>If A and B are both symmetric, then AB + BA will be symmetric, and AB &#8211; BA will be skew-symmetric.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"What_is_the_difference_between_a_symmetric_matrix_and_a_skew-symmetric_matrix\"><\/span>What is the difference between a symmetric matrix and a skew-symmetric matrix?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A symmetric matrix and a skew-symmetric matrix are the square matrices. But the major difference between them is:<\/p>\n<ol>\n<li>The symmetric matrix equals its transpose.<br \/>\n\u27f9If A is a symmetric matrix, then A = A<sup>T<\/sup><\/li>\n<li>Whereas a skew-symmetric matrix is a matrix whose transpose equals its negative.<br \/>\n\u27f9If A is a skew-symmetric matrix, then A<sup>T<\/sup> = \u2013 A.<\/li>\n<\/ol>\n<p>For better understanding of matrices, also read:<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td>Matrices<\/td>\n<td>Eigenvalues of a symmetric matrix<\/td>\n<td>Inverse of matrices<\/td>\n<\/tr>\n<tr>\n<td>Determinants<\/td>\n<td>Transpose of matrices<\/td>\n<td>Types of matrices<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Symmetric_and_Skew-symmetric_Matrix\"><\/span>FAQs on Symmetric and Skew-symmetric Matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Can_a_matrix_be_both_symmetric_and_skew-symmetric\"><\/span>Can a matrix be both symmetric and skew-symmetric?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNo, a matrix cannot be symmetric and skew-symmetric unless it is the null matrix (a matrix with zero elements). In a non-null matrix, the presence of non-zero diagonal elements in a symmetric matrix contradicts the property of having zero diagonal elements in a skew-symmetric matrix. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Are_symmetric_and_skew-symmetric_matrices_always_square_matrices\"><\/span>Are symmetric and skew-symmetric matrices always square matrices?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tBoth symmetric and skew-symmetric matrices are defined for square matrices only. In other words, their number of rows equals the number of columns. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Are_the_eigenvalues_of_a_symmetric_matrix_real\"><\/span>Are the eigenvalues of a symmetric matrix real?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tYes, all eigenvalues of a symmetric matrix are real. This property is known as the spectral theorem for symmetric matrices. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_relationship_between_the_eigenvectors_of_a_symmetric_matrix\"><\/span>What is the relationship between the eigenvectors of a symmetric matrix?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe eigenvectors corresponding to distinct eigenvalues of a symmetric matrix are orthogonal (perpendicular) to each other. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Can_a_matrix_be_both_symmetric_and_diagonal\"><\/span>Can a matrix be both symmetric and diagonal?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA diagonal matrix where all non-diagonal elements are zero is symmetric and diagonal. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Can_a_matrix_be_both_skew-symmetric_and_diagonal\"><\/span>Can a matrix be both skew-symmetric and diagonal?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNo, a matrix cannot be skew-symmetric and diagonal unless it is the null matrix. In a non-null matrix, the presence of non-zero diagonal elements contradicts the property of having zero diagonal elements in a skew-symmetric matrix. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_can_we_determine_if_a_matrix_is_symmetric_or_skew-symmetric\"><\/span>How can we determine if a matrix is symmetric or skew-symmetric?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo determine if a matrix is symmetric, we compare it to its transpose. If the matrix is equal to its transpose (A = A'), it is symmetric. To determine if a matrix is skew-symmetric, we compare it to the negation of its transpose. If the matrix equals the negation of its transpose (A = -A'), it is skew-symmetric. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Can a matrix be both symmetric and skew-symmetric?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"No, a matrix cannot be symmetric and skew-symmetric unless it is the null matrix (a matrix with zero elements). In a non-null matrix, the presence of non-zero diagonal elements in a symmetric matrix contradicts the property of having zero diagonal elements in a skew-symmetric matrix.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Are symmetric and skew-symmetric matrices always square matrices?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Both symmetric and skew-symmetric matrices are defined for square matrices only. In other words, their number of rows equals the number of columns.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Are the eigenvalues of a symmetric matrix real?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Yes, all eigenvalues of a symmetric matrix are real. This property is known as the spectral theorem for symmetric matrices.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the relationship between the eigenvectors of a symmetric matrix?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The eigenvectors corresponding to distinct eigenvalues of a symmetric matrix are orthogonal (perpendicular) to each other.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Can a matrix be both symmetric and diagonal?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A diagonal matrix where all non-diagonal elements are zero is symmetric and diagonal.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Can a matrix be both skew-symmetric and diagonal?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"No, a matrix cannot be skew-symmetric and diagonal unless it is the null matrix. In a non-null matrix, the presence of non-zero diagonal elements contradicts the property of having zero diagonal elements in a skew-symmetric matrix.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How can we determine if a matrix is symmetric or skew-symmetric?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To determine if a matrix is symmetric, we compare it to its transpose. If the matrix is equal to its transpose (A = A'), it is symmetric. To determine if a matrix is skew-symmetric, we compare it to the negation of its transpose. If the matrix equals the negation of its transpose (A = -A'), it is skew-symmetric.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Symmetric matrix Definition of a symmetric matrix: A square matrix A = [aij] is called a symmetric matrix if aij [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Symmetric and skew-symmetric matrix","_yoast_wpseo_title":"Symmetric and Skew-symmetric matrix: Definition, Example and Properties","_yoast_wpseo_metadesc":"Symmetric matrix and Skew Symmetric matrix both are square matrices but have different transpose properties. 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