The Collaborative International Dictionary
Adjoint \Ad"joint\, n. An adjunct; a helper. [Obs.]
Wiktionary
a. (context mathematics English) used in several situations with a meaning similar to helping n. 1 (context mathematics English) A matrix in which each element is the cofactor of an associated element of another matrix. 2 (context geometry English) A curve such that any point of another curve ''C'' of multiplicity ''r'' has multiplicity at least ''r''–1 on the adjoint. Sometimes the multiple points of ''C'' are required to be ordinary, and if this condition is not satisfied the term "sub-adjoint" is used. 3 An assistant mayor of a French commune.
Wikipedia
In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type
(Ax, y) = (x, By).Specifically, adjoint or adjunction may mean:
- Adjoint endomorphism of a Lie algebra
- Adjoint functors in category theory
- Hermitian adjoint (adjoint of a linear operator) in functional analysis
- For adjoint of a linear map, see transpose
- Adjoint representation of a Lie group
- Adjunction (category theory)
- Adjunction (field theory)
- Adjunction formula (algebraic geometry)
- Adjunction space in topology
- Conjugate transpose of a matrix in linear algebra
- Adjugate matrix, related to its inverse
- Adjoint equation
- The upper and lower adjoints of a Galois connection in order theory
- For the adjoint of a differential operator with general polynomial coefficients see differential operator
- Kleisli adjunction
- Monoidal adjunction
- Quillen adjunction
- Axiom of adjunction in set theory
Usage examples of "adjoint".
In addition to the pass, the adjoint had given Leigh a note to his cousin.
He would have done better for himself than by becoming adjoint to the maire of Arthenay.
Monsieur Tourrier showed the letter that he had received from his cousin, the adjoint at Arthenay.