Involutive Relation
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution is a bijection. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x \mapsto -x), reciprocation (x \mapsto 1/x), and complex conjugation (z \mapsto \bar z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the Beaufort polyalphabetic cipher. The composition of two involutions ''f'' and ''g'' is an involution if and only if they commute: . Involutions on finite sets The number of involutions, including the identity involution, on a set with elements is given by a recurrence relation found by Heinrich August Rothe in 1800: :a_0 = a_1 = 1 and a_n = a_ ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Involution
Involution may refer to: * Involute, a construction in the differential geometry of curves * ''Agricultural Involution: The Processes of Ecological Change in Indonesia'', a 1963 study of intensification of production through increased labour inputs * Involution (mathematics), a function that is its own inverse * Involution (medicine), the shrinking of an organ (such as the uterus after pregnancy) * Involution (esoterism), several notions of a counterpart to evolution * Involution (Meher Baba), the inner path of the human soul to the self * Involution algebra, a *-algebra: an algebra equipped with an involution * Involution (album), ''Involution'' (album), a 1998 album by multi-instrumentalist Michael Marcus, with the Jaki Byard trio * Involution (film), ''Involution'' (film), a 2018 Russian sci-fi drama film {{disambiguation ...
[...More Info...]     &