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Matrix Substraction

Tool to calculate matrix subtraction in algebra. The matrix subtraction is similar to the addition, it is obtained by subtracting the elements of each matrix.

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Matrix Substraction -

Tag(s) : MATRIX

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# Matrix Substraction

## Substraction of 2 Matrices

Tool to calculate matrix subtraction in algebra. The matrix subtraction is similar to the addition, it is obtained by subtracting the elements of each matrix.

### How to substract 2 matrices?

Substracting matrices is only possible with 2 matrices of the same shape.

Consider $$M_1=[a_{ij}]$$ a matrix of $$m$$ lines and $$n$$ columns (with $$m = n$$ in the case of a square matrix) and $$M_2=[b_{ij}]$$ another matrix of $$m$$ lines and $$n$$ columns.

The substraction of these 2 matrices $$M_1 - M_2 = [c_{ij}]$$ is an unchanged size matrix with $$m$$ lines and $$n$$ columns, and : $$\forall i, j : c_{ij} = a_{ij}-b_{ij}$$

For example :

$$\begin{pmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{pmatrix} - \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix} = \begin{pmatrix} 7-1 & 8-2 \\ 9-3 & 10-4 \\ 11-5 & 12-6 \end{pmatrix} = \begin{pmatrix} 6 & 6 \\ 6 & 6 \\ 6 & 6 \end{pmatrix}$$

### How to substract 2 matrices of distinct sizes?

The subtraction operation (or addition) of matrices is only defined with identical shapes matrices. Another operation called direct sum allows the use of matrices of different sizes and can be generalized to subtraction.