Definition:Standard Basis Matrix

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.

Also see

 * Definition:Standard Matrix Basis
 * Definition:Elementary Matrix