# Adjoint

From HandWiki

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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Original source: https://en.wikipedia.org/wiki/Adjoint.
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