Involution

Summary

An involution is a function from a set to itself that undoes itself: applying it twice gives back the starting point. Equivalently, it is a bijection that is its own inverse. Negation of numbers, complex conjugation, the complement of a set and the inverse map of a group are involutions. In algebra the word is also used for an involution that reverses a product, $(xy)^* = y^* x^*$, as in rings with involution.