Definition:Involution (Mapping)

Definition
An involution is a mapping which is its own inverse.

That is, if $f: A \to A$ is an involution, then:


 * $\forall x \in A: f \left({f \left({x}\right)}\right) = x$

Equivalently:


 * $\forall x,y \in A: f\left({x}\right) = y \implies f\left({y}\right) = x$

Also known as
An involution is also known as an involutive mapping or an involutive function.

An involutive mapping can also be found described as self-inverse.

Also see

 * Idempotent Mapping
 * Mapping is Involution iff Bijective and Symmetric