Involution

:See involution (philosophy) for the philosophy meaning.

General properties

The identity map is a trivial example of an involution. Common examples in mathematics of more interesting involutions include multiplication by −1 in arithmetic, the taking of reciprocals, complementation in set theory and complex conjugation.

Related Topics:
Identity map - Multiplication - Arithmetic - Reciprocal - Complementation - Set theory - Complex conjugation

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Another kind of inversion which is also an involution is circle inversion, which is a mapping of the plane into itself, which exchanges the interior and the exterior of a circle and takes the role in inversive geometry of the reflection in Euclidean geometry. In the complex plane it corresponds to taking the conjugate of the reciprocal.

Related Topics:
Circle inversion - Mapping - Plane - Circle - Inversive geometry - Euclidean geometry

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Other examples include include the ROT13 transformation, the Beaufort polyalphabetic cipher, and the Enigma cipher.

Related Topics:
ROT13 - Beaufort - Polyalphabetic cipher - Enigma - Cipher

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An involution is a kind of bijection.

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