Definition:Absolute Value of Mapping

Definition
Let $D$ be an ordered integral domain.

Let $\size {\, \cdot \,}_D$ denote the absolute value function on $D$.

Let $S$ be a set.

Let $f: S \to D$ be a mapping.

Then the absolute value of $f$, denoted $\size f_D: S \to D$, is defined as:


 * $\forall s \in S: \map {\size f_D} s := \size {\map f s}_D$

Absolute value thence is an instance of a pointwise operation on a mapping.

Examples

 * Definition:Absolute Value of Real-Valued Function

Also see

 * Absolute Value of Extended Real-Valued Function, not an example as $\overline \R$ is not an ordered integral domain
 * Definition:Pointwise Operation