# Conjugation

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*in Wiktionary, the free dictionary.***conjugation****Conjugation** or **conjugate** may refer to:

## Linguistics[edit]

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

## Mathematics[edit]

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

## Probability and statistics[edit]

- 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[edit]

- Sexual conjugation, a type of isogamy in unicellular eukaryotes
- Bacterial conjugation, 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, 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