Definition:Involution (Mapping)/Definition 3

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Definition

Let $A$ be a set.

Let $f: A \to A$ be a mapping on $A$.


Then $f$ is an involution if and only if $f$ is both a bijection and a symmetric relation.

That is, if and only if $f$ is a bijection such that $f = f^{-1}$.


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

  • Results about involutions can be found here.


Sources