Suppose that $\vect{u},\,\vect{v}\in\complex{m}$. The sum of $\vect{u}$ and $\vect{v}$ is the vector $\vect{u}+\vect{v}$ defined by \begin{align*} \vectorentry{\vect{u}+\vect{v}}{i} &=\vectorentry{\vect{u}}{i}+\vectorentry{\vect{v}}{i} &&1\leq i\leq m \end{align*}