Suppose that $B=\set{\vectorlist{v}{p}}$ is an orthonormal basis of the subspace $W$ of $\complex{m}$. For any $\vect{w}\in W$, \begin{equation*} \vect{w}= \innerproduct{\vect{v}_1}{\vect{w}}\vect{v}_1+ \innerproduct{\vect{v}_2}{\vect{w}}\vect{v}_2+ \innerproduct{\vect{v}_3}{\vect{w}}\vect{v}_3+ \cdots+ \innerproduct{\vect{v}_p}{\vect{w}}\vect{v}_p \end{equation*}