Matrix Product (Conventional)/Examples/Column Matrix All 0 except for One 1

Example of (Conventional) Matrix Product
Let $\mathbf A$ be a matrix of order $m \times n$.

For $1 \le i \le n$, let $\mathbf e_i$ be the column matrix of order $n \times 1$ defined as:
 * $e_k = \delta_{k i}$

where:
 * $e_k$ is the element $\mathbf e_i$ whose indices are $\tuple {k, 1}$
 * $\delta_{k i}$ denotes the Kronecker delta.

Then $\mathbf A \mathbf e_i$ is the column matrix which is equal to the $i$th column of $\mathbf A$.