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Matrix Subtraction

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 Subtraction -

Tag(s) : Matrix

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# Matrix Subtraction

## Subtraction 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 subtract 2 matrices?

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

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

### How to subtract 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.