View source for Adjoint

{{wiktionary}}
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:
* [[Transpose of a linear map|Adjoint of a linear map]], also called its transpose in case of matrices
* [[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
* [[Adjunction (rule of inference)]]

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[[Category:Mathematical terminology]]