Definition:Matrix/Column

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

For each $j \in \left[{1 \,.\,.\, n}\right]$, the columns of the matrix 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 $j = 1, 2, \ldots, n$.