Column Space

Definition: Column Space

The column space of a matrix $A\in F^{m\times n}$

$$A=\left[\begin{array}{ccc}\mid & \mid & \mid \\ {\vec{a}}_1& \cdots & {\vec{a}}_n\\ \mid & \mid & \mid \end{array}\right]$$

is the span $⟨{\vec{a}}_1,\cdots ,{\vec{a}}_n⟩$ of its columns.

Definition: Column Rank

The column rank of $A$ is the dimension of its column space.