Conjugation

From Wikipedia, the free encyclopedia

Conjugation may refer to:

• Grammatical conjugation, the modification of a verb from its basic form.
  • Latin conjugation, Spanish conjugation and the English verb, each with complex conjugation forms.
• Marriage, relationship between two or more individuals.

In mathematics:

• Complex conjugation, the operation which multiplies the imaginary part of a complex number by −1; see also conjugate element (field theory).
• The conjugate transpose of a matrix with complex entries is created by taking the transpose of the matrix and the complex conjugate of each entry.
• A conjugate in algebra is similar to a complex conjugate, but is used to rationalize the denominator of a fraction.
• In group theory, if a is an element of a group, then the map f(x) = axa⁻¹ is called conjugation by a. See inner automorphism, conjugacy class, conjugate closure, and conjugation of isometries in Euclidean space.
• Topological conjugation, which identifies equivalent dynamical systems.
• Conjugate points, in differential geometry.
• Conjugate prior, in probability theory, a family of prior probability distributions.

In science:

• In biology, transmission of DNA without fusion of gametes. This includes bacterial conjugation, which takes place without fusion; conjugation in ciliates, which involves fusion of nuclei but not cells; and conjugation in certain algae and fungi, which involves fusion of cells but not filaments.
• Conjugated system, in organic chemistry, a system of atoms covalently bonded with alternating single and multiple bonds.
• In immunology, a Conjugate vaccine
• Conjugate variables (thermodynamics), the internal energy of a system.
• In metabolism, conjugation is a biochemical process to bind a substance to an acid and thereby deactivating its biological activity, making it water-soluble, and facilitating its excretion.
• Conjugate quantities, in quantum physics, are observables that are linked by the Heisenberg uncertainty principle, such as position and momentum.