Suppose that $\ltdefn{T}{U}{V}$ and $\ltdefn{S}{V}{W}$ are linear transformations. Then the composition of $S$ and $T$ is the function $\ltdefn{(\compose{S}{T})}{U}{W}$ whose outputs are defined by \begin{equation*} \lt{(\compose{S}{T})}{\vect{u}}=\lt{S}{\lt{T}{\vect{u}}} \end{equation*}