Definition:Pointwise Addition of Linear Operators

Definition
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 is vector addition.

Specific Instances
Specific instantiations of this concept to particular vector spaces are as follows: