What is Subtraction of Matrices?

Matrix subtraction is an operation where corresponding elements of two matrices are subtracted from each other to form a new matrix. This operation is similar to matrix addition, but instead of adding the corresponding elements, they are subtracted.

For two matrices to be subtracted, they must have the same dimensions, meaning they must have the same number of rows and columns. If A and B are two matrices of the same dimensions, their subtraction is denoted as A − B.

Notation of Matrix Subtraction

Given two matrices A and B of the same size, the matrix subtraction A−B is defined as:

(A − B)_ij ​= A_ij​ − B_ij​

where A_ij​ and B_ij​ are the elements of matrices A and B at the i^th row and j^th column, respectively.

Condition for Matrix Subtraction

For matrix subtraction to be defined and valid, the following condition must be satisfied:

The two matrices must have the same dimensions, meaning they must have the same number of rows and the same number of columns.

Subtraction of matrices is addition of the negative of a matrix to another matrix which means A – B = A + (-B). The subtraction of the matrix is subtracting the corresponding row-column element of one matrix with same row-column element of another matrix.

In this article we will explore subtraction of matrices in detail. We will also solve some examples related to subtraction of matrices. Let’s start our learning on the topic “Subtraction of Matrices.”