Definition:Pointwise Multiplication

Definition
Let $S$ be a set, and let $f,g : S \to \R$ be real-valued functions.

Then the pointwise product of $f$ and $g$, $f \cdot g: S \to \R$, is defined by (for all $s \in S$):


 * $\left({f \cdot g}\right) \left({s}\right) := f \left({s}\right) \cdot g \left({s}\right)$

where the $\cdot$ on the right is real multiplication.

Pointwise multiplication thence is an instance of a pointwise operation on real-valued functions.

Also see

 * Pointwise Multiplication is Associative
 * Pointwise Multiplication is Commutative
 * Pointwise Operation on Real-Valued Functions