Suppose that $V$ is a vector space with a basis $B=\set{\vectorlist{v}{n}}$. Define a function $\ltdefn{\vectrepname{B}}{V}{\complex{n}}$ as follows. For $\vect{w}\in V$ define the column vector $\vectrep{B}{\vect{w}}\in\complex{n}$ by \begin{align*} \vect{w} &= \vectorentry{\vectrep{B}{\vect{w}}}{1}\vect{v}_1+ \vectorentry{\vectrep{B}{\vect{w}}}{2}\vect{v}_2+ \vectorentry{\vectrep{B}{\vect{w}}}{3}\vect{v}_3+ \cdots+ \vectorentry{\vectrep{B}{\vect{w}}}{n}\vect{v}_n \end{align*}