Scalar Matrix

A diagonal matrix whose diagonal elements are equal, is called a scalar matrix.

scalar matrices
Scalar Matrix

Scalar matrix is a square matrix and the number of rows is equal to the number of columns in it. So, a diagonal matrix is possible by the square matrix. A diagonal matrix contains elements only on the leading diagonal and remaining elements are zeros. In the same pattern, scalar matrices contain elements in principal diagonal but those elements are same.

M = e 1⁣1 0 0 0 0 e 2⁣2 0 0 0 0 e 3⁣3 0 0 0 0 e n⁣n

Therefore, the diagonal elements are same and non-diagonal elements are zero in scalar matrices.

e1⁣1  =  e2⁣2  =  e3⁣3  =   =  en⁣n

Example

A is a square matrix of order 4×4. It is formed by 16 elements. The matrix A is having nonzero elements on principal diagonal but having zeros as non-diagonal elements. Therefore, the square matrix A is recognized as a diagonal matrix.

A = 6 0 0 0 0 6 0 0 0 0 6 0 0 0 0 6

The diagonal matrix A contains same elements on the leading diagonal. Therefore, it is known as a scalar matrix.

Save (or) Share
Follow Math Doubts
Email subscription
Copyright © 2012 - 2017 Math Doubts, All Rights Reserved