Adjoint
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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 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)
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 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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