\begin{definition}[Definition:Pointwise Addition on Complex Vector Space]
Let $\C^n$ be a complex vector space.
Let $S$ and $T$ be linear operators on $\C^n$.
Then the '''pointwise sum of $S$ and $T$''' is defined as:
:$S + T: \C^n \to \C^n:$
::$\forall u \in \C^n: \map {\paren {S + T} } u := \map S u + \map T u$
where $+$ on the {{RHS}} is complex vector addition.
Thus '''pointwise addition''' on $\C^n$ is seen to be an instance of a pointwise addition of linear operators.
\end{definition}