# Conjugation

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**Conjugal**redirects here. For the type of prison visit, see conjugal visit.

**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**. See inner automorphism, conjugacy class, conjugate closure, and conjugation of isometries in Euclidean space.*a* - 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.
- A Conjugate element in field theory.

In the **biosciences**:

- 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.
- In immunology, a conjugate vaccine

- 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.

In **chemistry**:

- a conjugate acid-base pair is one base and one acid which differ from each other by one proton (
*H*^{+}), as defined by the Brønsted-Lowry acid-base theory - In organic chemistry, a conjugated system is a system of atoms covalently bonded with alternating single and multiple bonds.
- In biochemistry: (see metabolism above)

**In physics**:

- Conjugate variables (thermodynamics), the internal energy of a system.
- Conjugate quantities, in quantum physics, are observables that are linked by the Heisenberg uncertainty principle, such as position and momentum.