Definition:Standard Basis Matrix

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 $\left({i, j}\right)$th standard basis matrix is the $m \times n$ matrix which is $0$ everywhere except a $1$ at the $\left({i, j}\right)$th position.

Also see

 * Definition:Standard Matrix Basis
 * Definition:Elementary Matrix