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

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.

$M=\left[\begin{array}{ccccc}{e}_{1\⁣1}& 0& 0& \cdots & 0\\ 0& {e}_{2\⁣2}& 0& \cdots & 0\\ 0& 0& {e}_{3\⁣3}& \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0& 0& 0& \cdots & {e}_{n\⁣n}\end{array}\right]$

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

${e}_{1\⁣1}={e}_{2InvisibleComma;2}={e}_{3InvisibleComma;3}=\dots ={e}_{nInvisibleComma;n}$

$A$ is a square matrix of order $4\times 4$. 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.

$A=\left[\begin{array}{cccc}6& 0& 0& 0\\ 0& 6& 0& 0\\ 0& 0& 6& 0\\ 0& 0& 0& 6\end{array}\right]$

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

Copyright © 2012 - 2017 Math Doubts, All Rights Reserved