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Let $\mathbf A$ be an $m \times n$ matrix.

For each $j \in \left[{1 \,.\,.\, n}\right]$, the columns of $\mathbf A$ are the ordered $m$-tuples $c_j = \left({a_{1 j}, a_{2 j}, \ldots, a_{m j}}\right)$

where $c_j$ is called the $j$th column of $\mathbf A$.

A column of an $m \times n$ matrix can also be treated as a $m \times 1$ column matrix in its own right:

$c_j = \begin{bmatrix} a_{1 j} \\ a_{2 j} \\ \vdots \\ a_{m j} \end{bmatrix}$ for $j = 1, 2, \ldots, n$.

Also see