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

1. (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)