<\/span><\/h3>\nA system of m \u00d7 n numbers arranged in the form of a rectangular array having m rows and n columns is called an matrix of order m \u00d7 n.<\/p>\n
If A = [aij<\/sub> ]m x n<\/sub>\u00a0be any matrix of order m \u00d7 n then it is written in the form:<\/p>\n![\"Columns\"](\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/08\/columns.jpg\")
<\/p>\n
Horizontal lines are called rows and vertical lines are called columns.<\/p>\n
<\/span>Special Types of Matrices<\/span><\/h3>\n1. Square Matrix:<\/strong> An m \u00d7 n matrix for which m = n (The number of rows is equal to number of columns) is called square matrix. It is also called an n-rowed square matrix. i.e. A = [aij ]n \u00d7 n. The elements aij \u23d0 i = j, i.e. a11, a22…. are called DIAGONAL ELEMENTS and the line along which they lie is called PRINCIPLE DIAGONAL of matrix. Elements other than a11, a22, etc are called off-diagonal elements i.e. aij \u23d0 i \u2260 j<\/p>\n2. Scalar Matrix:<\/strong> A scalar matrix is a diagonal matrix with all diagonal elements being equal.<\/p>\n3. Unit Matrix or Identity Matrix:<\/strong> A square matrix each of whose diagonal elements is 1 and each of whose non-diagonal elements are zero is called unit matrix or an identity matrix which is denoted by I. Identity matrix is always square.<\/p>\n4. Null Matrix:<\/strong> The m \u00d7 n matrix whose elements are all zero is called null matrix. Null matrix is denoted by O. Null matrix need not be square. aij = 0 \u2200 i, j<\/p>\n5. Upper Triangular Matrix:<\/strong> An upper triangular matrix is a square matrix whose lower off-diagonal elements are zero, i.e. aij = 0 whenever i > j<\/p>\nIt is denoted by U.<\/p>\n
6. Lower Triangular Matrix:<\/strong> A lower triangular matrix is a square matrix whose upper off-diagonal triangular elements are zero, i.e. aij = 0 whenever i < j. The diagonal and lower off-diagonal elements may or may not be zero. . {aij = 0 if i< j<\/p>\nIt is denoted by L,<\/p>\n
7. Idempotent Matrix:<\/strong> A matrix A is called Idempotent if A2 = A.<\/p>\n8. Involuntary Matrix:<\/strong> A matrix A is called Involutory if A2 = I.<\/p>\n9. Nilpotent Matrix:<\/strong> A matrix A is said to be nilpotent of class x or index x if Ax = O and Ax \u2013 1 \u2260 O i.e. x is the smallest index which makes Ax = O.<\/p>\n10. Singular matrix:<\/strong> If the determinant of a matrix is zero, then matrix is called as singular matrix.<\/p>\n11. Row Matrix:<\/strong> A matrix with only one row is called as Row Matrix. A row matrix can have any number of columns i.e., it has an order 1 \u00d7 n where n \u2208 natural number.<\/p>\n12. Column Matrix:<\/strong> A matrix with only one column is called as column matrix. A column matrix can have any number of rows i.e., it has an order m \u00d7 1 where m \u2208 natural number.<\/p>\n","protected":false},"excerpt":{"rendered":"In this chapter, we shall discuss matrix algebra and its use in solving linear system of algebraic equations AX =<\/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":[1715,1713,1714,1712],"class_list":["post-5855","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","category-ee","tag-lower-triangular-matrix","tag-nilpotent-matrix","tag-null-matrix","tag-types-of-matrices"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5855","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=5855"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5855\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}