{"id":2193,"date":"2022-03-29T17:46:43","date_gmt":"2022-03-29T17:46:43","guid":{"rendered":"https:\/\/swatilathia.com\/?page_id=2193"},"modified":"2022-03-31T17:39:43","modified_gmt":"2022-03-31T17:39:43","slug":"matrix-its-types","status":"publish","type":"page","link":"https:\/\/swatilathia.com\/?page_id=2193","title":{"rendered":"Matrix &#038; its types"},"content":{"rendered":"<body>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a2cbf3b466c8\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a2cbf3b466c8\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#What_is_Matrix\" >What is Matrix?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Application_Area_of_Matrix\" >Application Area of Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Order_of_the_Matrix\" >Order of the Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-5\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-6\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-7\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Null_or_Zero_Matrix\" >Null or Zero 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:\/\/swatilathia.com\/?page_id=2193\/#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-9\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-10\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-11\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Identity_or_Unit_Matrix\" >Identity or Unit 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:\/\/swatilathia.com\/?page_id=2193\/#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-13\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-14\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Lower_Triangular_Matrix\" >Lower Triangular Matrix<\/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:\/\/swatilathia.com\/?page_id=2193\/#Transpose_of_Matrix\" >Transpose of Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#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-17\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Skew_Symmetric_Matrix\" >Skew Symmetric Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Singular_Matrix\" >Singular Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Idempotent_Matrix\" >Idempotent 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:\/\/swatilathia.com\/?page_id=2193\/#Nilpotent_Matrix\" >Nilpotent Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Orthogonal_Matrix\" >Orthogonal Matrix<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/swatilathia.com\/?page_id=2193\/#Equal_Matrix\" >Equal Matrix<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"What_is_Matrix\"><\/span>What is Matrix?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">In Mathematics, a Matrix (plural Matrices) is a rectangular array or table of integers organized in rows and columns. The numbers are referred to as the matrix\u2019s elements or entries. A matrix\u2019s size is determined\u00a0by the number of rows and columns it has.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Application_Area_of_Matrix\"><\/span>Application Area of Matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Matrices are used in a variety of fields, including Graph theory, Analysis and Geometry, Probability Theory and Statistics, Symmetries and Transformations in Physics, Linear Combinations of Quantum States, and Electronics.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Order_of_the_Matrix\"><\/span>Order of the Matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">If there are m rows and n columns, the matrix is said to be an \u201cm by n\u201d matrix, written \u201cm \u00d7 n.\u201d For example, <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"256\" height=\"134\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image.png?resize=256%2C134&#038;ssl=1\" alt=\"\" class=\"wp-image-2194\" loading=\"lazy\"><\/figure>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">m is row number means there are 2 rows and n is column number so there are 3 columns. So m x n = 2 x 3. <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Here 1 2 3 and 4 5 6 are rows (See horizontally). 1 4, 2 5, 3 6 are columns (See vertically). <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Let us take another example.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"151\" height=\"110\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-1.png?resize=151%2C110&#038;ssl=1\" alt=\"\" class=\"wp-image-2195\" loading=\"lazy\"><\/figure>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">As you can notice m=3 and n=3 so Order of the matrix is 3 x 3. You can also say, this is a square matrix as its no of rows and columns are equal.<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Here 4 5 6, 1 3 5, 2 6 1 are rows. 4 1 2, 5 3 6, 6 5 1 are columns<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Types_of_Matrices\"><\/span>Types of Matrices<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Row_Matrix\"><\/span>Row Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A matrix is said to be row matrix if it has one and only one row. For example, A = [ 4 5 9 ]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Column_Matrix\"><\/span>Column Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A matrix is said to be column matrix if it has one and only one column. For example, here A is a column matrix<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"91\" height=\"113\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-4.png?resize=91%2C113&#038;ssl=1\" alt=\"\" class=\"wp-image-2205\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Null_or_Zero_Matrix\"><\/span>Null or Zero Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A matrix is said to be Null or Zero matrix if all the elements of matrix are zero. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"94\" height=\"56\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-5.png?resize=94%2C56&#038;ssl=1\" alt=\"\" class=\"wp-image-2206\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Square_Matrix\"><\/span>Square Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A matrix is n x n matrix, the matrix having the same number of rows as columns. Here A is 2 x 2 square matrix<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"99\" height=\"62\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-6.png?resize=99%2C62&#038;ssl=1\" alt=\"\" class=\"wp-image-2207\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Diagonal_Matrix\"><\/span>Diagonal Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix in which all the elements except its principle diagonal are zero, is known as Diagonal Matrix. Here A is 3 x 3 Diagonal matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"120\" height=\"85\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-7.png?resize=120%2C85&#038;ssl=1\" alt=\"\" class=\"wp-image-2210\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Scalar_Matrix\"><\/span>Scalar Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A Diagonal matrix in which elements of its principle diagonal are equal, is known as Scalar Matrix. Here A is 3 x 3 scalar matrix, in which its diagonal elements are equal (10).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"126\" height=\"86\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-8.png?resize=126%2C86&#038;ssl=1\" alt=\"\" class=\"wp-image-2211\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Identity_or_Unit_Matrix\"><\/span>Identity or Unit Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A Scalar matrix in which elements of its principle diagonal are 1 (one), is known as Identity or Unit Matrix. Here I is 3 x 3 identity matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"103\" height=\"75\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-9.png?resize=103%2C75&#038;ssl=1\" alt=\"\" class=\"wp-image-2212\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Triangular_Matrix\"><\/span>Triangular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Upper_Triangular_Matrix\"><\/span>Upper Triangular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix, in which all the elements below principle diagonal are zero, is known as Upper Triangular Matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"105\" height=\"80\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-10.png?resize=105%2C80&#038;ssl=1\" alt=\"\" class=\"wp-image-2213\" loading=\"lazy\"><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Lower_Triangular_Matrix\"><\/span>Lower Triangular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix, in which all the elements above principle diagonal are zero, is known as Lower Triangular Matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"108\" height=\"76\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-11.png?resize=108%2C76&#038;ssl=1\" alt=\"\" class=\"wp-image-2214\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Transpose_of_Matrix\"><\/span>Transpose of Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">The transpose of a matrix is\u00a0found by interchanging its rows into columns or columns into rows.\u00a0If \u201cA\u201d is the given matrix, then the transpose of the matrix is represented by A\u2019 or A<sup>T<\/sup>. If matrix A is of order 3 x 2 then A\u2019 is of order 2 x 3. In below example, i just interchanged the rows into columns (or columns into rows).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"326\" height=\"98\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-13.png?resize=326%2C98&#038;ssl=1\" alt=\"\" class=\"wp-image-2228\" loading=\"lazy\" srcset=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-13.png?w=326&amp;ssl=1 326w, https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-13.png?resize=300%2C90&amp;ssl=1 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Symmetric_Matrix\"><\/span>Symmetric Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix A is said to be asymmetric matrix , if A = A\u2019.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"284\" height=\"92\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-15.png?resize=284%2C92&#038;ssl=1\" alt=\"\" class=\"wp-image-2230\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Skew_Symmetric_Matrix\"><\/span>Skew Symmetric Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix A is said to be asymmetric matrix , if A = \u2013 A\u2019.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"160\" height=\"91\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-16.png?resize=160%2C91&#038;ssl=1\" alt=\"\" class=\"wp-image-2231\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Singular_Matrix\"><\/span>Singular Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix A is said to be singular matrix , if | A | = 0. (determinant A is equal 0).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"499\" height=\"59\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-17.png?resize=499%2C59&#038;ssl=1\" alt=\"\" class=\"wp-image-2232\" loading=\"lazy\" srcset=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-17.png?w=499&amp;ssl=1 499w, https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-17.png?resize=300%2C35&amp;ssl=1 300w\" sizes=\"auto, (max-width: 499px) 100vw, 499px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Idempotent_Matrix\"><\/span>Idempotent Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Idempotent matrix is a square matrix which when multiplied by itself, gives back the same matrix. A matrix is said to be an\u00a0idempotent matrix\u00a0if A<sup>2<\/sup>\u00a0= A. Every identity matrix can be termed as an idempotent matrix.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"149\" height=\"82\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-18.png?resize=149%2C82&#038;ssl=1\" alt=\"\" class=\"wp-image-2234\" loading=\"lazy\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Nilpotent_Matrix\"><\/span>Nilpotent Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix\u00a0<em>A<\/em>\u00a0is called a nilpotent matrix, if\u00a0A<sup>n<\/sup>=0\u00a0for some positive integer n.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"333\" height=\"95\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-19.png?resize=333%2C95&#038;ssl=1\" alt=\"\" class=\"wp-image-2238\" loading=\"lazy\" srcset=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-19.png?w=333&amp;ssl=1 333w, https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-19.png?resize=300%2C86&amp;ssl=1 300w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/><\/figure>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Here A &amp; B both are nilpotent matrix. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Orthogonal_Matrix\"><\/span>Orthogonal Matrix<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A square matrix\u00a0A, such that\u00a0A\u00d7A<sup>T<\/sup>= I, is called an orthogonal matrix, where\u00a0<em>I<\/em>\u00a0is an identity matrix and\u00a0A<sup>T<\/sup>\u00a0is the transpose of matrix\u00a0A.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"325\" height=\"97\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-20.png?resize=325%2C97&#038;ssl=1\" alt=\"\" class=\"wp-image-2239\" loading=\"lazy\" srcset=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-20.png?w=325&amp;ssl=1 325w, https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-20.png?resize=300%2C90&amp;ssl=1 300w\" sizes=\"auto, (max-width: 325px) 100vw, 325px\" \/><\/figure>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Here if we do A x A<sup>T<\/sup> = I &amp; B X B<sup>T<\/sup> = I<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Equal_Matrix\"><\/span>Equal Matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">A matrix , say A = [a<sub>ij<\/sub>] is said to be equal to matrix B = [b<sub>ij<\/sub>], means A = B, if  A &amp; B have same order and a<sub>ij<\/sub> = b<sub>ij<\/sub> for each i &amp; j. Here A &amp; B both are equal matrix as each element of matrix A is exactly at same position in matrix B.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"303\" height=\"74\" src=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-21.png?resize=303%2C74&#038;ssl=1\" alt=\"\" class=\"wp-image-2240\" loading=\"lazy\" srcset=\"https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-21.png?w=303&amp;ssl=1 303w, https:\/\/i0.wp.com\/swatilathia.com\/wp-content\/uploads\/2022\/03\/image-21.png?resize=300%2C73&amp;ssl=1 300w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/figure>\n<\/body>","protected":false},"excerpt":{"rendered":"<p>What is Matrix? In Mathematics, a Matrix (plural Matrices) is a rectangular array or table of integers organized in rows and columns. The numbers are referred to as the matrix\u2019s elements or entries. A matrix\u2019s size is determined\u00a0by the number of rows and columns it has. Application Area of Matrix Matrices are used in a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-2193","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2193"}],"version-history":[{"count":8,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2193\/revisions"}],"predecessor-version":[{"id":2241,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2193\/revisions\/2241"}],"wp:attachment":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}