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...

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

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

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 * :...

Maths History. Retrieved 2025-04-19. "Cremona group - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2025-05-30. "A propos des travaux...

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, 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...

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...

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

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

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

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...

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

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

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

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

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

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...

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

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...

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}}...

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...

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...

form and the seventh of the form (22.q). a Lucas number. a telephone or involution number, the number of different ways of connecting 6 points with pairwise...

count involutions (elements of order 2) in G. Perhaps more important is another result that the authors derive from the same count of involutions, namely...

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;...

In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the...

group but respectively a commutative monoid and a commutative monoid with involution. A wheel is an algebraic structure ( W , 0 , 1 , + , ⋅ , / ) {\displaystyle...