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 complex analysis *

Conjugate (graph theory) In the mathematical discipline of graph theory, the line graph of an undirected graph is another graph that represents the adjacencies between edges of . is constructed in the following way: for each edge in , make a vertex in ; for every ...

, 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 i ...

, 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), the image of an element under the conjugation homomorphisms ** Conjugate closure, 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-definite. The conjugate gradient method is often implemented as an iter ...

, 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 viewpoin ...

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

Probability and statistics

* Conjugate prior, 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 functions and statistical mechanics

Science

* Sexual conjugation, 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 bacteria ...

, a mechanism of exchange of genetic material between bacteria * Conjugate vaccine, 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 lik ...

, 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 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 represent ...

, a system of atoms covalently bonded with alternating single and multiple bonds * Conjugate variables (thermodynamics), 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