{"id":5862,"date":"2025-08-06T11:29:32","date_gmt":"2025-08-06T05:59:32","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=5862"},"modified":"2025-08-06T11:29:32","modified_gmt":"2025-08-06T05:59:32","slug":"classification-of-real-matrices","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/linear-algebra\/classification-of-real-matrices","title":{"rendered":"Classification of Real Matrices"},"content":{"rendered":"<p>Real matrices can be classified into the following three types based on the relationship between AT and A.<\/p>\n<p>1. Symmetric Matrices (AT = A)<br \/>\n2. Skew Symmetric Matrices (AT = \u2013A)<br \/>\n3. Orthogonal Matrices (AT = A\u20131 or AAT = I)<\/p>\n<p><strong> 1. Symmetric Matrix:<\/strong> A square matrix A= [aij ] is said to be symmetric if its (i, j)th elements is same as its (j, i)th element i.e., aij = aji for all i &amp; j.<\/p>\n<p>In a symmetric matrix, AT = A<\/p>\n<p><strong>2.\u00a0 Skew Symmetric Matrix:<\/strong> A square matrix A = [aij ] is said to be skew symmetric if (i, j)th elements of A is the negative of the (j, i)th elements of A if aij = \u2013aji \u2200 i, j.<\/p>\n<p>In a skew symmetric matrix AT = \u2013 A.<br \/>\nA skew symmetric matrix must have all 0\u2019s in the diagonal.<\/p>\n<p><strong>3. Orthogonal Matrix:<\/strong> A square matrix A is said be orthogonal if:<br \/>\nAT = A\u20131 \u21d2 AAT = AA\u20131 = I. Thus A will be an orthogonal matrix if, AAT = I = ATA<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Real matrices can be classified into the following three types based on the relationship between AT and A. 1. Symmetric<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1711,5],"tags":[1719,1720,1721],"class_list":["post-5862","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","category-ee","tag-orthogonal-matrix","tag-skew-symmetric-matrix","tag-symmetric-matrix"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=5862"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5862\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}