Suppose that $\ltdefn{T}{U}{V}$ and $\ltdefn{S}{U}{V}$ are two linear transformations with the same domain and codomain. Then their sum is the function $\ltdefn{T+S}{U}{V}$ whose outputs are defined by \begin{equation*} \lt{(T+S)}{\vect{u}}=\lt{T}{\vect{u}}+\lt{S}{\vect{u}} \end{equation*}