Definition:Standard Matrix Basis

Definition
Let $R$ be a ring with unity.

Let $m, n \ge 1$ be positive integers.

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

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

Also see

 * Standard Matrix Basis is Basis
 * Dimension of Matrix Space
 * Definition:Vectorization of Matrix