A square matrix B b mxm is said to be a diagonal matrix if

Last updated: 10/6/2023

A square matrix B b mxm is said to be a diagonal matrix if all its non diagonal elements are zero that is a matrix B b mxm is said to be a diagonal matrix if b 0 when i j For example A 4 B of order 1 2 3 respectively v Scalar matrix For example A diagonal matrix is said to be a scalar matrix if its diagonal elements a that is a square matrix B b x is said to be a scalar matrix when i j when i j for some constant k A 3 B 1 1 C 0 b 0 ij b k C 0 coffe 0 are scalar matrices of order 1 2 and 3 respectively identity matrix if a kira of For example 1 3 0 1 1 O 0 0 20 0 03 vi Identity matrix A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an identity matrix In other words the square matrix A a x is an 1 if i j if i j 1 are diagonal matrices We denote the identity matrix of order n by I When order is clear from the context we simply write it as I 1 00 0 1 0 00 1 e equal are identity matrices of order 1 2 and 3 Rationalised 2023 24 respectively Observe that a scalar matrix is an identity matrix when k 1 But every identity matrix is clearly a scalar matrix 0 0 For example 0 0 0 zero matrix by O Its order will be clear from the context MATRICES vii Zero matrix A matrix is said to be zero matrix or null matrix if all its elements are zero 3 3 1 Equality of matrices Definition 2 Two matrices A a and B b are said to be equal if i they are of the same order 41 0 0 are all zero matrices We denote ii each element of A is equal to the corresponding element of B that is a b for all i and j