Suppose that $A$ is an $m\times n$ matrix with columns $\vectorlist{A}{n}$. Then the column space of $A$, written $\csp{A}$, is the subset of $\complex{m}$ containing all linear combinations of the columns of $A$, \begin{equation*} \csp{A}=\spn{\set{\vectorlist{A}{n}}} \end{equation*}