Definition:Standard Basis Matrix

Definition
Let $R$ be a ring with unity.

Let $n$ be a positive integer.

Let $i, j \in \left\{ {1, \ldots, n}\right\}$.

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

Also see

 * Definition:Elementary Matrix