NotesonMathematics-1021

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Notes on Mathematics - 1021Peeyush Chandra, A. K. Lal, V. Raghavendra, G. Santhanam1Supported by a grant from MHRD2ContentsI Linear Algebra71 Definition of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . Special Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . Operations on Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . Multiplication of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . Some More Special Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . Submatrix of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . Block Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Matrices over Complex Numbers.

Definition 1.2.7 (Additive Inverse) Let Abe an m×nmatrix. 1. Then there exists a matrix Bwith A+ B= 0.This matrix Bis called the additive inverse of A,and is denoted by −A= (−1)A. 2. Also, for the matrix 0m×n,A+0 = 0+A= A.Hence, the matrix 0m×n

  Inverse