Adjoint

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)