Conjugation or conjugate may refer to:

Linguistics

* Grammatical conjugation, the modification of a verb from its basic form * Emotive conjugation or Russell's conjugation, the use of loaded language

Mathematics

* Complex conjugation, the change of sign of the imaginary part of a complex number * Conjugate (square roots), the change of sign of a square root in an expression * Conjugate element (field theory), a generalization of the preceding conjugations to roots of a polynomial of any degree *

Conjugate transpose In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m \times n complex matrix \boldsymbol is an n \times m matrix obtained by transposing \boldsymbol and applying complex conjugate on each entry (the complex c ...

, the complex conjugate of the transpose of a matrix *

Harmonic conjugate In mathematics, a real-valued function u(x,y) defined on a connected open set \Omega \subset \R^2 is said to have a conjugate (function) v(x,y) if and only if they are respectively the real and imaginary parts of a holomorphic function f(z) of ...

in complex analysis * Conjugate (graph theory), an alternative term for a line graph, i.e. a graph representing the edge adjacencies of another graph *In group theory, various notions are called conjugation: **

Inner automorphism In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the ''conjugating element''. They can be realized via simple operations from within the group it ...

, a type of conjugation homomorphism **

Conjugation Conjugation or conjugate may refer to: Linguistics * Grammatical conjugation, the modification of a verb from its basic form * Emotive conjugation or Russell's conjugation, the use of loaded language Mathematics * Complex conjugation, the chang ...

in group theory, related to matrix similarity in linear algebra **

Conjugation (group theory) In mathematics, especially group theory, two elements a and b of a group are conjugate if there is an element g in the group such that b = gag^. This is an equivalence relation whose equivalence classes are called conjugacy classes. In other ...

, the image of an element under the conjugation homomorphisms **

Conjugate closure In group theory, the normal closure of a subset S of a group G is the smallest normal subgroup of G containing S. Properties and description Formally, if G is a group and S is a subset of G, the normal closure \operatorname_G(S) of S is the ...

, the image of a subgroup under the conjugation homomorphisms * Conjugate words in combinatorics; this operation on strings resembles conjugation in groups *

Isogonal conjugate __notoc__ In geometry, the isogonal conjugate of a point with respect to a triangle is constructed by reflecting the lines about the angle bisectors of respectively. These three reflected lines concur at the isogonal conjugate of . (Th ...

, in geometry * Conjugate gradient method, an algorithm for the numerical solution of particular systems of linear equations *

Conjugate points In differential geometry, conjugate points or focal points are, roughly, points that can almost be joined by a 1-parameter family of geodesics. For example, on a sphere, the north-pole and south-pole are connected by any meridian. Another viewpoi ...

, in differential geometry *

Topological conjugation In mathematics, two functions are said to be topologically conjugate if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy, and related-but-distinct of flows, are important in the study of iterated func ...

, which identifies equivalent dynamical systems *

Convex conjugate In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation, Fenchel transformatio ...

, the ("dual") lower-semicontinuous convex function resulting from the Legendre–Fenchel transformation of a "primal" function

Probability and statistics

Conjugate prior In Bayesian probability theory, if the posterior distribution p(\theta \mid x) is in the same probability distribution family as the prior probability distribution p(\theta), the prior and posterior are then called conjugate distributions, and th ...

, in Bayesian statistics, a family of probability distributions that contains a prior and the posterior distributions for a particular likelihood function (particularly for one-parameter exponential families) * Conjugate pairing of probability distributions, in the Fourier-analytic theory of

characteristic function In mathematics, the term "characteristic function" can refer to any of several distinct concepts: * The indicator function of a subset, that is the function ::\mathbf_A\colon X \to \, :which for a given subset ''A'' of ''X'', has value 1 at points ...

s and statistical mechanics

Science

Sexual conjugation Isogamy is a form of sexual reproduction that involves gametes of the same morphology (indistinguishable in shape and size), found in most unicellular eukaryotes. Because both gametes look alike, they generally cannot be classified as male or fe ...

, a type of isogamy in unicellular eukaryotes * Bacterial conjugation, a mechanism of exchange of genetic material between bacteria *

Conjugate vaccine A conjugate vaccine is a type of subunit vaccine which combines a weak antigen with a strong antigen as a carrier so that the immune system has a stronger response to the weak antigen. Vaccines are used to prevent diseases by invoking an immune ...

, in immunology *

Conjugation (biochemistry) Bioconjugation is a chemical strategy to form a stable covalent link between two molecules, at least one of which is a biomolecule. Function Recent advances in the understanding of biomolecules enabled their application to numerous fields like ...

, covalently linking a biomolecule with another molecule * Conjugate (acid-base theory), a system describing a conjugate acid-base pair * Conjugated system, a system of atoms covalently bonded with alternating single and multiple bonds *

Conjugate variables (thermodynamics) In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy or pressure and volume or chemical potential and particle number. In fact, all thermodynamic potentials ...

, pairs of variables that always change simultaneously * Conjugate quantities, observables that are linked by the Heisenberg uncertainty principle * Conjugate focal plane, in optics

Linguistics

Mathematics

Probability and statistics

Science

See also