Suppose that $\ltdefn{T}{U}{V}$ is a linear transformation, $B$ is a basis for $U$ of size $n$, and $C$ is a basis for $V$ of size $m$. Then the range of $T$ is isomorphic to the column space of $\matrixrep{T}{B}{C}$, \begin{equation*} \rng{T}\isomorphic\csp{\matrixrep{T}{B}{C}} \end{equation*}