{"id":5858,"date":"2025-08-05T12:26:31","date_gmt":"2025-08-05T06:56:31","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=5858"},"modified":"2025-08-05T12:26:31","modified_gmt":"2025-08-05T06:56:31","slug":"matrix-operations","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/linear-algebra\/matrix-operations","title":{"rendered":"Equality of Two Matrices"},"content":{"rendered":"

Two matrices<\/strong><\/p>\n

A = [aij ] and B = [bij ] are said to be equal if,<\/p>\n

    \n
  1. They are of same size.<\/li>\n
  2. The elements in the corresponding places of two matrices are the same i.e., aij = bij for each pair of subscripts i and j.<\/li>\n<\/ol>\n

    Addition of Matrices<\/strong><\/p>\n

    Two matrices A and B are compatible for addition only if they both have exactly the same size say m \u00d7 n. Then their sum is defined to be the matrix of the type m \u00d7 n obtained by adding corresponding elements of A and B. Thus if, A = [aij ]m \u00d7 n & B = [bij ]m \u00d7 n then A + B = [aij + bij ]m \u00d7 n.<\/p>\n

    Substraction of Two Matrices<\/strong><\/p>\n

    If A and B are two m \u00d7 n matrices, then we define, A \u2013 B = A + (\u2013B).
    \nThus the difference A \u2013 B is obtained by subtracting from each element of A corresponding elements of B.<\/p>\n

    Multiplication of a Matrix by a Scalar<\/strong><\/p>\n

    Let A be any m \u00d7 n matrix and k be any real number called scalar. The m \u00d7 n matrix obtained by multiplying every element of the matrix A by k is called scalar multiple of A by k and is denoted by kA.
    \n\u21d2 If A = [aij ]m \u00d7 n then Ak = kA =[kA]m \u00d7 n.<\/p>\n

    Multiplication of Two Matrices<\/strong><\/p>\n

    Let A = [aij ]m \u00d7 n; B = [bjk]n \u00d7 p be two matrices such that the number of columns in A is equal to the number
    \nof rows in B<\/p>\n

    Trace of a Matrix<\/strong><\/p>\n

    Let A be a square matrix of order n. The sum of the elements lying along principal diagonal is called the trace of A denoted by Tr(A).<\/p>\n

    \"<\/p>\n

    Transpose of a Matrix<\/strong><\/p>\n

    Let A = [aij ]m \u00d7 n. Then the n \u00d7 m matrix obtained from A by changing its rows into columns and its columns into rows is called the transpose of A and is denoted by A\u2032 or AT.<\/p>\n

    \"<\/p>\n

    Conjugate of a Matrix<\/strong><\/p>\n

    The matrix obtained from given matrix A on replacing its elements by the corresponding conjugate complex numbers is called the conjugate of A and is denoted by A.<\/p>\n

    Transposed Conjugate of Matrix<\/strong><\/p>\n

    The transpose of the conjugate of a matrix A is called transposed conjugate of A and is denoted by A\u03b8 or A* or ( )T A . It is also called conjugate transpose of A. This is also known as tranjugate of A<\/p>\n","protected":false},"excerpt":{"rendered":"

    Two matrices A = [aij ] and B = [bij ] are said to be equal if, They are of<\/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":[1717,1716,1718],"class_list":["post-5858","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","category-ee","tag-conjugate-of-a-matrix","tag-transpose-of-a-matrix","tag-transposed-conjugate-of-matrix"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5858","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=5858"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5858\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5858"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5858"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5858"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}