Matrix addition

The sum of two matrices of the same dimensions (number of rows and columns) is the term by term sum: if $A$, $B$ are $(m \times n)$ matrices then the sum $A+B$ is also an $(m \times n)$ matrix with $(A+B)_{ij} = A_{ij} + B_{ij}$ for $i=1,\ldots,m$ and $j = 1,\ldots n$.

See also: Matrix multiplication, Matrix ring