Definition:Standard Basis Matrix
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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 $\tuple {i, j}$th standard basis matrix is the $m \times n$ matrix which is $0$ everywhere except a $1$ at the $\tuple {i, j}$th indices.