Matrix algebra
= Matrix algebra
{title2=$M_n(A)$}
For an <associative algebra> $A$, its matrix algebra $M_n(A)$ consists of all $n$ by $n$ <matrices> over $A$, with ordinary matrix multiplication. If $A=k$ is a <field>, this is $\operatorname{End}_k(k^n)$ and is a <central simple algebra>. Full matrix algebras over division rings are the factors in the <Artin–Wedderburn theorem>.