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:
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Adjoint of a linear map, also called its transpose
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Hermitian adjoint (adjoint of a linear operator) in functional analysis
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Adjoint endomorphism of a Lie algebra
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Adjoint representation of a Lie group
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Adjoint functors in category theory
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Adjunction (field theory)
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Adjunction formula (algebraic geometry) In mathematics, especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside that variety. It is often used to deduce facts about varieties embedd ...
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Adjunction space In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another. Specifically, let ''X'' and ''Y'' be topological spaces, and let ''A'' be a subspace of ' ...
in topology
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Conjugate transpose of a matrix in linear algebra
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Adjugate matrix, related to its inverse
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Adjoint equation
* The upper and lower adjoints of a
Galois connection In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets). Galois connections find applications in various mathematical theories. They generalize the funda ...
in order theory
* The adjoint of a
differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and return ...
with general polynomial coefficients
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Kleisli adjunction
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Monoidal adjunction
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Quillen adjunction
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Axiom of adjunction in set theory
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Adjunction (rule of inference)
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. I ...
{{sia, mathematics
Mathematical terminology