Conjugation Explained

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, 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

• 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, 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

See also

• Conjugal (disambiguation)
• Conjoint