Definition:Standard Basis Matrix

Definition
Let $R$ be a ring with unity.

Let $n$ be a positive integer.

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

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

Also see

 * Definition:Elementary Matrix