Row Space

Definition: Row Space

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

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

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

Definition: Row Rank

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