\begin{definition}[Definition:Pointwise Addition of Linear Operators]
Let $V$ be a vector space.
Let $\map \LL V$ denote the set of linear operators on $V$.
:$+: \map \LL V \times \map \LL V \to \map \LL V: \forall S, T \in \map \LL V:$
::$\forall u \in V: \map {\paren {S + T} } u := \map S u + \map T u$
where $+$ on the {{RHS}} is vector addition.
\end{definition}