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)