Conjugation or conjugate may refer to:

Linguistics

Grammatical conjugation In linguistics, conjugation () is the creation of derived forms of a verb from its principal parts by inflection (alteration of form according to rules of grammar). For instance, the verb ''break'' can be conjugated to form the words ''break'', ...

, the modification of a verb from its basic form *

Emotive conjugation In rhetoric, emotive or emotional conjugation (also known as Russell's conjugation) mimics the form of a grammatical conjugation of an irregular verb to illustrate humans' tendency to describe their own behavior more charitably than the behavior ...

or Russell's conjugation, the use of loaded language

Mathematics

Complex conjugation In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...

, the change of sign of the imaginary part of a complex number *

Conjugate (square roots) In mathematics, the conjugate of an expression of the form a+b\sqrt d is a-b\sqrt d, provided that \sqrt d does not appear in and . One says also that the two expressions are conjugate. In particular, the two solutions of a quadratic equation are ...

, the change of sign of a square root in an expression *

Conjugate element (field theory) In mathematics, in particular field theory, the conjugate elements or algebraic conjugates of an algebraic element , over a field extension , are the roots of the minimal polynomial of over . Conjugate elements are commonly called conjuga ...

, 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 con ...

, 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 th ...

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 itse ...

, 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 i ...

, 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 . (This ...

, in geometry *

Conjugate gradient method In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterativ ...

, 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 transformation ...

, 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 Bacterial conjugation is the transfer of genetic material between bacterial cells by direct cell-to-cell contact or by a bridge-like connection between two cells. This takes place through a pilus. It is a parasexual mode of reproduction in bacteri ...

, 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 conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton () to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a ...

, a system describing a conjugate acid-base pair *

Conjugated system In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as ...

, 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 Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation� ...

, observables that are linked by the Heisenberg uncertainty principle *

Conjugate focal plane In optics, a conjugate plane or conjugate focal plane of a given plane ''P'', is the plane ''P′'' such that points on ''P'' are imaged on ''P′''. If an object is moved to the point occupied by its image, then the moved object's new image will ...

, in optics

Linguistics

Mathematics

Probability and statistics

Science

See also