Conjugation

Conjugation or conjugate may refer to:

Linguistics

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
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

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

Sexual conjugation, a type of isogamy in eukaryotes
Conjugation (microbiology), a mechanism of exchange of genetic material between bacteria
Conjugation (biochemistry), the turning of substances into a hydrophilic state in the body
Conjugate vaccine, in immunology

Conjugation (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), the internal energy of a system
Conjugate quantities, observables that are linked by the Heisenberg uncertainty principle
Conjugate focal plane, in optics