Definition:Standard Matrix Basis
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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 $\set {1, \ldots, m} \times \set {1, \ldots, n}$.