Adjoint

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 of a linear map, also called its transpose
* Hermitian adjoint (adjoint of a linear operator) in functional analysis
* Adjoint endomorphism of a Lie algebra
* Adjoint representation of a Lie group
* Adjoint functors in 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
* The adjoint of a differential operator with general polynomial coefficients
* Kleisli adjunction
* Monoidal adjunction
* Quillen adjunction
* Axiom of adjunction in set theory

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