Matrix Addition

Denote the sum of two Matrices ${\hbox{\sf A}}$ and ${\hbox{\sf B}}$ (of the same dimensions) by ${\hbox{\sf C}}={\hbox{\sf A}}+{\hbox{\sf B}}$. The sum is defined by adding entries with the same indices

$$c_{ij} \equiv a_{ij}+b_{ij}$$

over all $i$ and $j$. For example,

$$\left[{\matrix{a_{11} & a_{12}\cr a_{21} & a_{22}\cr}}\right... ... & a_{12}+b_{12}\cr a_{21}+b_{21} & a_{22}+b_{22}\cr}}\right].$$

Matrix addition is therefore both Commutative and Associative.

See also Matrix, Matrix Multiplication