Definition:Pointwise Addition of Complex-Valued Functions

Definition

Let $S$ be a non-empty set.

Let $f, g: S \to \C$ be complex-valued functions.

Then the pointwise sum of $f$ and $g$ is defined as:

$f + g: S \to \C:$

$\forall s \in S: \map {\paren {f + g} } s := \map f s + \map g s$

where $+$ on the right hand side is complex addition.

Thus pointwise addition is seen to be an instance of pointwise operation on complex-valued functions.

Also see

• Pointwise Addition on Complex-Valued Functions is Associative
• Pointwise Addition on Complex-Valued Functions is Commutative

• Definition:Pointwise Operation on Complex-Valued Functions