adjoint

Etymology
From, from late 19th C; see also. .

In the case of category theory (which brings together concepts from numerous fields), the term is often confounded with and the relationship is called an. The origin of any particular usage may therefore be uncertain.

Adjective

 * 1)  That is related to another functor by an adjunction.
 * 2)  Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.
 * 1)  Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.

Usage notes
The adjoint operator, or Hermitian transpose, of an operator generalises the concept of transpose conjugate of a matrix. (See )

In the case of an representation of a Lie group, the representation in question describes the group's elements as linear transformations of its Lie algebra, itself considered as a vector space. The representation is obtained by differentiating ("linearising") the group action of conjugation (i.e., differentiating the function x → gxg-1 for each element g).

The representation of a Lie algebra is the differential of the adjoint representation of a Lie group at the identity element of the group.

In relation to functors in category theory (and therefore in numerous fields of mathematics), the term is often synonymous with and the functors are said to be related by an. Functors may be left or right adjoint (adjunct).

Translations

 * Esperanto: adjunkta
 * German:
 * Spanish:

Noun

 * 1)  The transpose of the cofactor matrix of a given square matrix.
 * 2)  Transpose conjugate.
 * 3)  Hermitian conjugate.
 * 4)  A functor related to another functor by an adjunction.
 * 5)  A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.
 * 6) An assistant to someone who holds a position in the military or civil service.
 * 7) An assistant mayor of a French commune.
 * 1) An assistant mayor of a French commune.
 * 1) An assistant mayor of a French commune.
 * 1) An assistant mayor of a French commune.

Translations

 * German: Adjungierte
 * Spanish: matriz de adjuntos, matriz de cofactores


 * Bulgarian: ,
 * Slovak:

Noun

 * 1) deputy, assistant
 * 2)  adjunct