Conjugation

Conjugation or conjugate may refer to:

• Grammatical conjugation, the modification of a verb from its basic form
• Conjugation, sexual relations within marriage

Mathematics

• Conjugate (algebra), used to rationalize the denominator of a fraction
• Conjugate element (field theory), a generalization of complex conjugation
• Complex conjugation, the operation that multiplies the imaginary part of a complex number by −1
  • conj, a function in the C programming language or MATLAB that computes the complex conjugate.
• The conjugate transpose of a matrix
• Harmonic conjugate in complex analysis
• Isogonal conjugate
• In group theory, various notions are called conjugation:
  • Inner automorphism, a type of conjugation homomorphism
  • Conjugacy class, the image of an element under the conjugation homomorphisms
  • Conjugate closure, the image of a subgroup under the conjugation homomorphisms
  • Conjugation of isometries in Euclidean space, an explicit description of the images of elements under conjugation in a special case
• Topological conjugation, which identifies equivalent dynamical systems
• Conjugate points, in differential geometry
• Conjugate prior, in probability theory, a family of prior probability distributions
• Convex conjugate, generalization of the Legendre transformation, also known as Legendre-Fenchel transformation or Fenchel transformation
• Conformal conjugation in complex dynamics

Biology

• Conjugation (biochemistry), the turning of substances into a hydrophilic state in the body
• Bacterial conjugation, a transfer of DNA without fusion
• Conjugate vaccine, in immunology
• Sexual conjugation, a type of isogamy in eukaryotes

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, such as position and momentum
• Conjugate focal plane