Definition:Involution (Mapping)

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

That is, $f: A \to A$ is an involution precisely when:


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

Equivalently:


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

That the definitions are equivalent is proven in Characterization of Involution.

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

 * Mapping is Involution iff Bijective and Symmetric