Define a Scalar Matrix

Q. Define a Scalar Matrix?

Ans:  Scalar matrix is a special matrix or a square matrix. Having a constant value for all the elements of the diagonal and the other elements of the matrix are zero. So from this definition, we know the diagonal components of the scalar network are equivalent or similar.

If the diagonal element of a scalar matrix is one, then it becomes an identity matrix. The scalar matrix is obtained by multiplying the identity matrix with a numeric constant value. So, we can say that a scalar matrix is a multiple of an identity matrix with any scalar quantity. for example, if we consider k as a numeric constant value, then our scalar matrix would be 

K*1 0 0 0 1 0 0 0 1 =k 0 0 0 k 0 0 0 k 

constant*identify matrix = scalar matrix

The scalar matrix has an equal number of rows and columns; hence it is also known as a square matrix. The order of the scalar matrix is n*n.

Other than scalar matrices, there are many other types of matrices also as row matrix, column matrix, square matrix, diagonal matrix, null matrix, upper triangular matrix, lower triangular matrix, and an identity matrix. The only difference between a diagonal matrix and a scalar matrix is the principle of the diagonal element. 

As by diagonal matrix, all the elements are zero except diagonal elements, so by this statement, it is proven that the null matrix is not a scalar matrix. In an identity matrix, the diagonal elements are all equal to 1, and in the scalar matrix, all the diagonal elements are equal to a constant value. Hence we can say that all matrices differ in some manner, and some are the same.

When we work with frameworks of matrices, we allude to genuine numbers as scalars. The term scalar matrix denotes a matrix of the form k where k is scalar, and I am the identity matrix. These matrices are generally used in various branches of mathematics.