Matrix - Column Space

The column space of a matrix is the span of its columns. It is denoted as $\mathrm{Col}A$ for a matrix $A$.

More formally, a matrix $A$ represented as:

$$A=\left[\begin{array}{cccc}\overrightarrow{a_1}& \overrightarrow{a_2}& \cdots & \overrightarrow{a_n}\end{array}\right],\overrightarrow{a_i}\in {\mathbb{R}}^m$$

The column space of $A$ is defined as:

$$\mathrm{Col}A=\mathrm{span}\{\overrightarrow{a_1},\overrightarrow{a_2},\dots ,\overrightarrow{a_n}\}$$