Conjugation

Conjugation or conjugate may refer to:

• Grammatical conjugation, the modification of a verb from its basic form

Mathematics

• Conjugate (algebra), used to rationalize the denominator of a fraction
• Complex conjugation, the involution multiplying the imaginary part of a complex number by −1
• Conjugate element (field theory), a generalization of complex conjugation
• Conjugate transpose of a matrix, especially the Hermitian 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
• Conformal conjugation in complex dynamics

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

Biology

• 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

Chemistry

• 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

Physics

• 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

See also

• Conjugal (disambiguation)
• All pages with titles containing conjugation
• All pages with titles containing conjugate