Definition:Standard Matrix Basis

Definition

Let $R$ be a ring with unity.

Let $m,n\geq1$ be positive integers.

Let $i, j \in \left\{ {1, \ldots, m}\right\} \times \{ 1, \ldots, n\}$.

The standard matrix basis of $m\times n$ matrices over $R$ is the ordered basis of standard basis matrices ordered by the colexicographic order on $\left\{ {1, \ldots, m}\right\} \times \{ 1, \ldots, n\}$.