Matrix addition

In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. However, there are other operations which could also be considered as a kind of addition for matrices, thedirect sum and the Kronecker sum.

Entrywise sum
The usual matrix addition is defined for two matrices of the same dimensions. The sum of two m × n (pronounced "m by n") matrices A and B, denoted by A + B, is again an m × n matrix computed by adding corresponding elements:

For example:

We can also subtract one matrix from another, as long as they have the same dimensions. A − B is computed by subtracting corresponding elements of A and B, and has the same dimensions as A and B. For example: