\begin{definition}[Definition:Matrix/Column]
Let $\mathbf A$ be an $m \times n$ matrix.
For each $j \in \closedint 1 n$, the '''columns''' of $\mathbf A$ are the ordered $m$-tuples:
: $c_j = \tuple {a_{1 j}, a_{2 j}, \ldots, a_{m j} }$
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 $j = 1, 2, \ldots, n$.
\end{definition}