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 of ...

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), 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, the complex conjugate of the transpose of a matrix * Harmonic conjugate 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 change ...

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 wo ...

, 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, in geometry *

Conjugate gradient method In mathematics, the conjugate gradient method is an algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a c ...

, 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 viewpo ...

, in differential geometry * Topological conjugation, which identifies equivalent dynamical systems * Convex conjugate, 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 ...

, 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 ...

, 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 bacter ...

, 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 immun ...

, in immunology * Conjugation (biochemistry), 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 ...

, 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

Linguistics

Mathematics

Probability and statistics

Science

See also