In mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse, f(f(x)) = x for all x in the domain...

up involution in Wiktionary, the free dictionary. Involution may refer to: Involution (mathematics), a function that is its own inverse Involution algebra...

generalization of idempotence to binary relations Idempotent (ring theory) Involution (mathematics) Iterated function List of matrices Nilpotent Pure function Referential...

identity |−x| = |x|). Monoid Inverse function Involution (mathematics) Multiplicative inverse Reflection (mathematics) Reflection symmetry Semigroup Gallian...

may happen that an algebra admits no involution. Look up * or star in Wiktionary, the free dictionary. In mathematics, a *-ring is a ring with a map * :...

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...

structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. In other cases...

In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person...

inverse Involution (mathematics), a function that is its own inverse (when applied twice, the starting value is obtained) Inversion (discrete mathematics),...

In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism...

In mathematics, a Fricke involution is the involution of the modular curve X0(N) given by τ → –1/Nτ. It is named after Robert Fricke. The Fricke involution...

category theory, a branch of mathematics, a dagger category (also called involutive category or category with involution) is a category equipped with...

axis (a horizontal reflection) would look like b. A reflection is an involution: when applied twice in succession, every point returns to its original...

Maria (2002), Geometry of the plane Cremona maps, Lecture Notes in Mathematics, vol. 1769, Berlin, New York: Springer-Verlag, doi:10.1007/b82933,...

matrix. These are both symmetric, they are their own inverses (see involution (mathematics)), and each have determinant −1. This latter property makes them...

by the matrix A n × n {\displaystyle {\mathbf {A}}_{n\times n}} is an involution if and only if A 2 = I , {\displaystyle {\mathbf {A}}^{2}={\mathbf {I}}...

In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation...

semisimple Lie algebra has a Cartan involution, and any two Cartan involutions are equivalent. A Cartan involution on s l n ( R ) {\displaystyle {\mathfrak...

the classical involution theorem The infinite Thompson groups F, T and V studied by the logician Richard Thompson. Outside of mathematics, it may also...

In mathematical finite group theory, the classical involution theorem of Aschbacher (1977a, 1977b, 1980) classifies simple groups with a classical involution...

Cayley–Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension.: 45  Hurwitz's theorem states...

The function is linear. Involution: Exclusive or with one specified input, as a function of the other input, is an involution or self-inverse function;...

+ cx3 + d. Samuel Jeake introduced the term indices in 1696. The term involution was used synonymously with the term indices, but had declined in usage...

first place. Every involution on a finite set with an odd number of elements has a fixed point; more generally, for every involution on a finite set of...

morphism R : X → Y {\displaystyle R\colon X\to Y} is associated with an anti-involution, i.e. a morphism R ∘ : Y → X {\displaystyle R^{\circ }\colon Y\to X} with...

group is said to be of component type if for some centralizer C of an involution, C/O(C) has a component (where O(C) is the core of C, the maximal normal...

distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e. an involution that additionally satisfies De Morgan's laws)...

Semigroup with involution Jacobson, Nathan (1943). The Theory of Rings. Mathematical Surveys and Monographs. Vol. 2. American Mathematical Society. p. 16...

opposite category defining an involution on the category of small categories, the opposite simplicial sets defines an involution on the category of simplicial...

identity; for this reason, the resulting operator is called an Atkin–Lehner involution. If e and f are both Hall divisors of N, then We and Wf commute modulo...