{"id":663966,"date":"2023-07-06T14:16:11","date_gmt":"2023-07-06T08:46:11","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=663966"},"modified":"2025-05-15T15:17:27","modified_gmt":"2025-05-15T09:47:27","slug":"types-of-matrices","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/","title":{"rendered":"What are the Matrices? and Its Types"},"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'><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Types_of_Matrices\" title=\"Types of Matrices\">Types 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-2\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Types_of_Matrices-2\" title=\"Types of Matrices\">Types of Matrices<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Row_Matrix\" title=\"Row Matrix\">Row Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Column_Matrix\" title=\"Column Matrix\">Column Matrix<\/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\/types-of-matrices\/#Square_Matrix\" title=\"Square Matrix\">Square Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Zero_or_Null_Matrix\" title=\"Zero or Null Matrix\">Zero or Null Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Singleton_Matrix\" title=\"Singleton Matrix\">Singleton Matrix<\/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\/types-of-matrices\/#Horizontal_Matrix\" title=\"Horizontal Matrix\">Horizontal Matrix<\/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\/types-of-matrices\/#Vertical_Matrix\" title=\"Vertical Matrix\">Vertical Matrix<\/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\/types-of-matrices\/#Diagonal_Matrix\" title=\"Diagonal Matrix\">Diagonal 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\/types-of-matrices\/#Scalar_Matrix\" title=\"Scalar Matrix\">Scalar Matrix<\/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\/types-of-matrices\/#Unit_Matrix_or_Identity_Matrix\" title=\"Unit Matrix or Identity Matrix\">Unit Matrix or Identity Matrix<\/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\/types-of-matrices\/#Equal_Matrices\" title=\"Equal Matrices\">Equal Matrices<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Equality_of_Matrices_Conditions\" title=\"Equality of Matrices Conditions:\">Equality of Matrices Conditions:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Triangular_Matrix\" title=\"Triangular Matrix\">Triangular Matrix<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Upper_Triangular_Matrix\" title=\"Upper Triangular Matrix\">Upper Triangular Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Lower_Triangular_Matrix\" title=\"Lower Triangular Matrix\">Lower Triangular Matrix<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Symmetric_and_Skew_Symmetric_Matrices\" title=\"Symmetric and Skew Symmetric Matrices\">Symmetric and Skew Symmetric Matrices<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Symmetric_matrix\" title=\"Symmetric matrix:\">Symmetric matrix:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#Skew-Symmetric_Matrix\" title=\"Skew-Symmetric Matrix\">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-21\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#FAQs_on_Types_of_Matrices\" title=\"FAQs on Types of Matrices\">FAQs on Types of Matrices<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#What_is_a_square_matrix\" title=\"What is a square matrix?\">What is a square matrix?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#What_is_a_diagonal_matrix\" title=\"What is a diagonal matrix?\">What is a diagonal matrix?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#What_is_a_symmetric_matrix\" title=\"What is a symmetric matrix?\">What is a symmetric matrix?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/#What_is_a_skew-symmetric_matrix\" title=\"What is a skew-symmetric matrix?\">What is a skew-symmetric matrix?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>A Matrix is a rectangular array of m \u00d7 n numbers, which may be either real or complex. These numbers are set in the form of m horizontal lines and n vertical lines and altogether defined as a matrix of order m by n, and also it is represented as m \u00d7 n Matrix&#8217;. The rectangular array is enclosed in either () or [] brackets. This article will discuss the types of Matrices.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Types_of_Matrices\"><\/span>Types of Matrices<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>There are different types of Matrices based on the number of elements, the number of rows and columns or their order.<br \/>\nDifferent matrices based on the different factors are summarised in the table below.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td><strong>Type of Matrix<\/strong><\/td>\n<td><strong>Details<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Row Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>1\u00d7n<\/sub><\/td>\n<\/tr>\n<tr>\n<td>Column Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>m\u00d71<\/sub><\/td>\n<\/tr>\n<tr>\n<td>Zero or Null Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>mxn,<\/sub> where, a<sub>ij<\/sub> = 0<\/td>\n<\/tr>\n<tr>\n<td>Singleton Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>mxn<\/sub> where, m = n =1<\/td>\n<\/tr>\n<tr>\n<td>Horizontal Matrix<\/td>\n<td>[a<sub>ij<\/sub>]<sub>mxn<\/sub> where n &gt; m<\/td>\n<\/tr>\n<tr>\n<td>Vertical Matrix<\/td>\n<\/tr>\n<tr>\n<td>Square Matrix<\/td>\n<td>[a<sub>ij<\/sub>]<sub>mxn<\/sub> where, m = n<\/td>\n<\/tr>\n<tr>\n<td>Diagonal Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>] when i \u2260 j<\/td>\n<\/tr>\n<tr>\n<td>Scalar Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>mxn<\/sub><br \/>\n[a<sub>ij<\/sub>] = k when i = j<br \/>\n[a<sub>ij<\/sub>] = 0 when i \u2260 j<\/td>\n<\/tr>\n<tr>\n<td>Identity (Unit) Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>mxn<\/sub> where,<br \/>\n[a<sub>ij<\/sub>] = 1 when i = j<br \/>\n[a<sub>ij<\/sub>] = 0 when i \u2260 j<\/td>\n<\/tr>\n<tr>\n<td>Equal Matrix<\/td>\n<td>A = [a<sub>ij<\/sub>]<sub>mxn<\/sub> and B = [b<sub>ij<\/sub>]<sub>rxs<\/sub> where, a<sub>ij<\/sub> = <sub>bij, m = r, and n = s<\/sub><\/td>\n<\/tr>\n<tr>\n<td>Triangular Matrices<\/td>\n<td>Can be either upper triangular (a<sub>ij<\/sub> = 0, when i &gt; j) or lower triangular (a<sub>ij<\/sub> = 0 when i &lt; j)<\/td>\n<\/tr>\n<tr>\n<td>Singular Matrix<\/td>\n<td>|A| = 0<\/td>\n<\/tr>\n<tr>\n<td>Non-Singular Matrix<\/td>\n<td>|A| \u2260 0<\/td>\n<\/tr>\n<tr>\n<td>Symmetric Matrices<\/td>\n<td>A = [a<sub>ij<\/sub>] where, a<sub>ij<\/sub> = a<sub>ji<\/sub><\/td>\n<\/tr>\n<tr>\n<td>Skew-Symmetric Matrices<\/td>\n<td>A = [a<sub>ij<\/sub>] where, a<sub>ij<\/sub> = a<sub>ji<\/sub><\/td>\n<\/tr>\n<tr>\n<td>Hermitian Matrix<\/td>\n<td>A = A<sup>\u03b8<\/sup><\/td>\n<\/tr>\n<tr>\n<td>Skew \u2013 Hermitian Matrix<\/td>\n<td>A<sup>\u03b8<\/sup> = -A<\/td>\n<\/tr>\n<tr>\n<td>Orthogonal Matrix<\/td>\n<td>A A<sup>T<\/sup> = In = AT A<\/td>\n<\/tr>\n<tr>\n<td>Idempotent Matrix<\/td>\n<td>A<sup>2<\/sup> = A<\/td>\n<\/tr>\n<tr>\n<td>Involuntary Matrix<\/td>\n<td>A<sup>2<\/sup> = I, A<sup>-1<\/sup> = A<\/td>\n<\/tr>\n<tr>\n<td>Nilpotent Matrix<\/td>\n<td>\u2203 p \u2208 N such that A<sup>P<\/sup> = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Matrices-2\"><\/span>Types of Matrices<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>On the basis of the number of rows and columns, the matrices are classified as:<\/p>\n<ol>\n<li><strong>Row Matrices<\/strong><\/li>\n<li><strong>Column Matrices<\/strong><\/li>\n<li><strong>Square Matrices<\/strong><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Row_Matrix\"><\/span><strong>Row Matrix<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A matrix consisting of only one row is a row matrix.<br \/>\nThus A = [aij]mxn is a row matrix if m = 1.<br \/>\nThis matrix is called a Row matrix because it has only one row, and the order of a row matrix will hence be 1 \u00d7 n.<\/p>\n<p><strong>For example,<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>A = [8 9 7 6] is a row matrix of order 1 x 4.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Column_Matrix\"><\/span>Column Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A matrix consisting of only one column is a column matrix.<br \/>\nThus, A = [aij]mxn is a column matrix if n = 1. Hence, the order is m \u00d7 1.<\/p>\n<p><strong>For example,<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663968\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/column-matrix.png\" alt=\"column matrix\" width=\"142\" height=\"241\" \/><\/p>\n<p>is a column matrix of order 3 x 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Square_Matrix\"><\/span>Square Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If the matrix has an equal number of rows and the number of columns, then it is called a square matrix.<\/p>\n<p>Thus, A = [aij]mxn is a square matrix if m = n.<\/p>\n<p><strong>For example,<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663969\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/square-matrix.png\" alt=\"square matrix\" width=\"289\" height=\"271\" \/><\/p>\n<p>is a square matrix of order 3 \u00d7 3.<\/p>\n<p><strong>Trace of matrix:<\/strong> The sum of the diagonal elements in a square matrix A is called the trace of matrix A, and which is denoted by tr(A).<\/p>\n<p><strong>On the basis of the value entered in the row and column, the matrices are classified as:<\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Zero_or_Null_Matrix\"><\/span>Zero or Null Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The matrix with all the elements as zero is called a zero matrix and is generally denoted by 0.<\/p>\n<p>Thus, A = [aij]mxn is a zero-matrix if aij = 0 for all i and j.<\/p>\n<p><strong>For example,<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-663970\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/null-matrix-300x224.png\" alt=\"null matrix\" width=\"300\" height=\"224\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/null-matrix-300x224.png 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/null-matrix.png 306w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>is a zero matrix of 3 x 3 order.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Singleton_Matrix\"><\/span>Singleton Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If the matrix has a single element, it is called a singleton matrix.<\/p>\n<p>Thus, A = [aij]mxn is a singleton matrix if m = n = 1.<\/p>\n<p>For example:<\/p>\n[8], [9], [a], [ ] are singleton matrices.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Horizontal_Matrix\"><\/span>Horizontal Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A matrix of m x n order is defined as a horizontal matrix if n &gt; m.<\/p>\n<p><strong>For example,<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663971\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Horizontal-Matrix.png\" alt=\"Horizontal Matrix\" width=\"280\" height=\"193\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vertical_Matrix\"><\/span>Vertical Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A matrix of order m x n is defined as a vertical matrix if m &gt; n.<\/p>\n<p><strong>For example,<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663972\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/verticla-matrix.png\" alt=\"vertical matrix\" width=\"153\" height=\"241\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Diagonal_Matrix\"><\/span>Diagonal Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If all the elements of the square matrix except the principal diagonal are zero, then it is said to be a diagonal matrix.<\/p>\n<p>Thus, a square matrix A = [aij] is a diagonal matrix if aij = 0,when i \u2260 j.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663973\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Diagonal-Matix.png\" alt=\"Diagonal Matrix\" width=\"268\" height=\"246\" \/><\/p>\n<p>is a diagonal matrix of order 3 x 3.<\/p>\n<p><strong>Students must note that:<\/strong><\/p>\n<ol style=\"list-style-type: lower-roman;\">\n<li>A diagonal matrix will always be a square matrix.<\/li>\n<li>The diagonal elements are characterised by aij in general where i = j.<\/li>\n<li>Also, a diagonal matrix can have only a single diagonal.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Scalar_Matrix\"><\/span>Scalar Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If all the elements in the diagonal of a diagonal matrix are equal, it is called a scalar matrix. Thus, a square matrix<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-663974\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Scalar-Matrix.png\" alt=\"Scalar Matrix\" width=\"253\" height=\"243\" \/><\/p>\n<p>where k is a constant.<\/p>\n<p>Also, it is wondered, what if all the diagonal elements are equal to 1? Will this kind of Matrix be a scalar or diagonal matrix?<\/p>\n<p>The answer to this query is quite simple, this type of Matrix will still be a scalar matrix and obviously a diagonal matrix too. These matrices are known as the identity matrix.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Unit_Matrix_or_Identity_Matrix\"><\/span>Unit Matrix or Identity Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>If all the elements of a principal diagonal in a diagonal matrix are 1, it is called a unit matrix.<\/p>\n<p>A unit matrix of order n is denoted by In.<\/p>\n<p><strong>For example:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663975\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/unit-matrix.png\" alt=\"unit matrix\" width=\"289\" height=\"255\" \/><\/p>\n<p>To conclude,<\/p>\n<ul>\n<li>All identity matrices are always scalar matrices<\/li>\n<li>All scalar matrices are precisely diagonal matrices<\/li>\n<li>All diagonal matrices are basically square matrices<\/li>\n<li>Also note that the converse of the above mentioned statements is not true for any of the cases.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Equal_Matrices\"><\/span>Equal Matrices<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Equal matrices are those matrices which are equal in terms of their elements.<\/p>\n<p>The conditions for matrix equality are discussed below.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equality_of_Matrices_Conditions\"><\/span>Equality of Matrices Conditions:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Two matrices A and B are said to be equal if they are of the same order and their corresponding elements are equal, i.e. two matrices A = [aij]m\u00d7n and B = [bij]r\u00d7s are equal if:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>m = r, i.e., the number of rows in A = the number of rows in B.<\/li>\n<li>n = s, i.e. the number of columns in A = the number of columns in B<\/li>\n<li>aij = bij, for i = 1, 2, \u2026.., m and j = 1, 2, \u2026.., n, i.e. the corresponding<\/li>\n<\/ol>\n<p>elements are equal;<\/p>\n<p>For example, Matrices<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-663976\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Equality-of-Matrices-Conditions-300x210.png\" alt=\"Equality of Matrices Conditions\" width=\"300\" height=\"210\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Equality-of-Matrices-Conditions-300x210.png 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Equality-of-Matrices-Conditions.png 447w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>are not equal because their orders are not the same.<\/p>\n<p>But, If<\/p>\n<p>Matrix A<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-663977\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/marix-A-and-B-144x300.png\" alt=\"matrix A and B\" width=\"144\" height=\"300\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/marix-A-and-B-144x300.png 144w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/marix-A-and-B.png 292w\" sizes=\"(max-width: 144px) 100vw, 144px\" \/><\/p>\n<p>Matrix A and B are equal matrices then,<\/p>\n<p>a=1, b=1, c=1<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Triangular_Matrix\"><\/span>Triangular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A square matrix is said to be a <strong>triangular matrix<\/strong> if the elements above or below the principal diagonal are zero, and there are of two types:<\/p>\n<ol>\n<li>\n<h4><span class=\"ez-toc-section\" id=\"Upper_Triangular_Matrix\"><\/span>Upper Triangular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/li>\n<\/ol>\n<p>A square matrix [aij] is called an upper triangular matrix, if aij = 0, when i &gt; j is an upper triangular matrix of order 3 x 3.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663978\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Upper-Triangular-Matrix.png\" alt=\"Upper Triangular Matrix\" width=\"256\" height=\"273\" \/><\/p>\n<ol>\n<li>\n<h4><span class=\"ez-toc-section\" id=\"Lower_Triangular_Matrix\"><\/span>Lower Triangular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/li>\n<\/ol>\n<p>A square matrix is called a lower triangular matrix, if aij = 0 when i &lt; j.<\/p>\n<p>is a lower triangular matrix of order 3 x 3.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663979\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Lower-Triangular-Matrix.png\" alt=\"Lower Triangular Matrix\" width=\"301\" height=\"256\" \/><\/p>\n<p>Singular Matrix and Non-Singular Matrix<\/p>\n<ul>\n<li>Matrix A is said to be a singular matrix if it\u2019s determinant |A| = 0<\/li>\n<li>Matrix A is said to be a singular matrix if it\u2019s determinant |A| \u2260 0<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Symmetric_and_Skew_Symmetric_Matrices\"><\/span>Symmetric and Skew Symmetric Matrices<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Symmetric_matrix\"><\/span>Symmetric matrix:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A square matrix A = [aij] is called a symmetric matrix if aij = aji, for all i,j values;<br \/>\nEg.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663980\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Symmetric-matrix.png\" alt=\"Symmetric matrix\" width=\"256\" height=\"237\" \/><\/p>\n<p>is symmetric<\/p>\n<p>Note: matrix A is symmetric if A\u2019 = A (where \u2018A\u2019 is the transpose of the matrix)<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Skew-Symmetric_Matrix\"><\/span>Skew-Symmetric Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A square matrix A = [aij] is a skew-symmetric matrix if aij = aji, for all<\/p>\n<p>values of i,j.<\/p>\n[putting j = i] aii = 0<\/p>\n<p>Thus, in a skew-symmetric matrix, all diagonal elements are zero.<\/p>\n<p>E.g.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-663981\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/07\/Skew-Symmetric-Matrix.png\" alt=\"Skew-Symmetric Matrix\" width=\"264\" height=\"247\" \/><br \/>\nare skew-symmetric matrices.<\/p>\n<p><strong>Note:<\/strong> A square matrix A is a skew-symmetric matrix A\u2019 = -A.<\/p>\n<p><strong>Some Important Conclusions on Symmetric and Skew-Symmetric Matrices<\/strong><\/p>\n<ul>\n<li>any square matrix,<\/li>\n<\/ul>\n<ul style=\"list-style-type: circle;\">\n<li>then A + A\u2019 is a symmetric matrix<\/li>\n<li>And, A \u2013 A\u2019 is a skew-symmetric matrix.<\/li>\n<\/ul>\n<ul>\n<li>Every square matrix can be uniquely expressed as the sum of a symmetric and skew-symmetric matrix.<\/li>\n<li>If A and B are symmetric matrices, then A &amp; B commute, i.e. AB is symmetric AB = BA.<\/li>\n<li>The matrix B\u2019AB is symmetric or skew-symmetric in correspondence if A is symmetric or skew-symmetric.<\/li>\n<li>All positive integral powers of a symmetric matrix are symmetric.<\/li>\n<li>Positive odd integral powers of a skew-symmetric matrix are skew-symmetric, and positive even integral powers of a skew-symmetric matrix are symmetric.<\/li>\n<\/ul>\n<p>Also, Orthogonal Matrix, Idempotent Matrix, Involuntary Matrix and Nilpotent Matrix are the special matrices whose conditions are mentioned below.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td>Orthogonal Matrix<\/td>\n<td>A AT = In = AT A<\/td>\n<\/tr>\n<tr>\n<td>Idempotent Matrix<\/td>\n<td>A2 = A<\/td>\n<\/tr>\n<tr>\n<td>Involuntary Matrix<\/td>\n<td>A2 = I, A-1 = A<\/td>\n<\/tr>\n<tr>\n<td>Nilpotent Matrix<\/td>\n<td>\u2203 p \u2208 N such that AP = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Types_of_Matrices\"><\/span>FAQs on Types of Matrices<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=\"What_is_a_square_matrix\"><\/span>What is a square 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\tA square matrix is a matrix with an equal number of rows and columns. In other words, it has the same number of rows as columns. For example, a 3x3 matrix or a 5x5 matrix is a square 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=\"What_is_a_diagonal_matrix\"><\/span>What is a diagonal 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\tA diagonal matrix is a square matrix where all the elements outside the main diagonal (the diagonal from the top left to the bottom right) are zero. The main diagonal elements can be any values, including zero.\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_a_symmetric_matrix\"><\/span>What is 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\tA symmetric matrix is a square matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A^T = A. This means that the elements above and below the main diagonal are mirror images of 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=\"What_is_a_skew-symmetric_matrix\"><\/span>What is a skew-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\tA skew-symmetric matrix is a square matrix where the transpose of the matrix is equal to the negation of the matrix. In other words, if A is a skew-symmetric matrix, then A^T = -A. This means that the elements above the main diagonal are the negations of the elements below the main 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\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\": \"What is a square matrix?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A square matrix is a matrix with an equal number of rows and columns. In other words, it has the same number of rows as columns. For example, a 3x3 matrix or a 5x5 matrix is a square 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\": \"What is a diagonal matrix?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A diagonal matrix is a square matrix where all the elements outside the main diagonal (the diagonal from the top left to the bottom right) are zero. The main diagonal elements can be any values, including zero.\"\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 a symmetric matrix?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A symmetric matrix is a square matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A^T = A. This means that the elements above and below the main diagonal are mirror images of 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\": \"What is a skew-symmetric matrix?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A skew-symmetric matrix is a square matrix where the transpose of the matrix is equal to the negation of the matrix. In other words, if A is a skew-symmetric matrix, then A^T = -A. This means that the elements above the main diagonal are the negations of the elements below the main diagonal.\"\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>A Matrix is a rectangular array of m \u00d7 n numbers, which may be either real or complex. These numbers [&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":"Types of matrices","_yoast_wpseo_title":"Types of Matrices - DefinitioN, Diagoram and Solved Examlpes","_yoast_wpseo_metadesc":"A Matrix is a rectangular array of m \u00d7 n numbers, Row Types of Matrices - Row Matrices, Column Matrices, and Square Matrices","custom_permalink":"topics\/types-of-matrices\/"},"categories":[8594,8591],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Types of Matrices - DefinitioN, Diagoram and Solved Examlpes<\/title>\n<meta name=\"description\" content=\"A Matrix is a rectangular array of m \u00d7 n numbers, Row Types of Matrices - Row Matrices, Column Matrices, and Square Matrices\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Types of Matrices - 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