, ... , a nn are said to constitute the diagonal , of the matrix A. Thus, if Then the elements of the diagonal of A are , , . (iv) Diagonal matrix A square matrix B = [ b ij ] m × m is said to be a diagonal matrix if all its non diagonal elements are zero, that is a matrix B = [ b ij ] m × m is said to be a diagonal matrix if b ij = , when i ≠ j .
For example, A = [ ], , . C , are diagonal matrices of order , , , respectively. (v) Scalar matrix A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal, that is, a square matrix B = [ b ij ] n × n is said to be a scalar matrix if b ij = , when i ≠ j b ij = k , when i = j , for some constant k . For example A = [ ], , C are scalar matrices of order , and , respectively.
(vi) Identity matrix A square matrix in which elements in the diagonal are all and rest are all zero is called an identity matrix . In other words, the square matrix A = [ a ij ] n × n is an identity matrix, if if if ij i j i j = ≠ We denote the identity matrix of order n by I n . When order is clear from the context, we simply write it as I. For example [ ], , are identity matrices of order , and , respectively.
Observe that a scalar matrix is an identity matrix when k = . But every identity matrix is clearly a scalar matrix. MATRICES (vii) Zero matrix A matrix is said to be zero matrix or null matrix if all its elements are zero. For example, [ ], , , [ , ] are all zero matrices.
We denote zero matrix by