Denote the sum of two matrices and (of the same dimensions) by . The sum is defined by adding entries with the same indices

over all and . For example,

Matrix addition is therefore both commutative and associative.

Denote the sum of two matrices and (of the same dimensions) by . The sum is defined by adding entries with the same indices

over all and . For example,

Matrix addition is therefore both commutative and associative.

Weisstein, Eric W. "Matrix Addition."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MatrixAddition.html