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Tool to calculate matrix additions in computer algebra. The sum of N matrices is generally obtained by summing the elements of each matrix.

Answers to Questions

How to add 2 matrices?

The addition of matrices can only be done with 2 matrices of the same shape (size).

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

The sum of these 2 matrices \( M_1 + M_2 = [c_{ij}] \) is a matric of the same size, ie. \( m \) lines and \( n \) columns, with : $$ \forall i, j : c_{ij} = a_{ij}+b_{ij} $$

The addition operation (or sum) for matrices can only be done with same size matrices. Nevertheless, there is the direct sum operation, which can be used with distinct size matrices.

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