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) is a rhetorical technique used to create an intrinsic bias towards or against a piece of information. Bias is created by using the emotional connotation of a word ...

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 numbers, then the complex conjugate of a + bi is 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 conjug ...

, 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 \mathbf is an n \times m matrix obtained by transposing \mathbf and applying complex conjugation to each entry (the complex conjugate ...

, 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 Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within thos ...

, a type of conjugation homomorphism **

Conjugacy class 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 ...

in group theory, related to matrix similarity in linear algebra ** Conjugation (group theory), 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 for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an it ...

, an algorithm for the numerical solution of particular systems of linear equations * Conjugate points, in differential geometry * Topological conjugation, 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 transformati ...

, 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, given a likelihood function p(x \mid \theta), the posterior distribution p(\theta \mid x) is in the same probability distribution family as the prior probability distribution p(\theta), the prior and posteri ...

, 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, a type of isogamy in unicellular eukaryotes *

Bacterial conjugation Bacterial conjugation is the transfer of genetic material between Bacteria, 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 cycle, parasexual mode ...

, a mechanism of exchange of genetic material between bacteria * Conjugate vaccine, in immunology * Conjugation (biochemistry), covalently linking a biomolecule with another molecule * Conjugate (acid-base theory), a system describing a conjugate acid-base pair *

Conjugated system In physical organic 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 Chemical stability, stability. It is Reson ...

, a system of atoms covalently bonded with alternating single and multiple bonds * Conjugate variables (thermodynamics), pairs of variables that always change simultaneously * Conjugate quantities, observables that are linked by the Heisenberg uncertainty principle * Conjugate focal plane, in optics *

Charge conjugation In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C- ...

Linguistics

Mathematics

Probability and statistics

Science

See also