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 endomorphism of a Lie algebra
  • Adjunction (field theory)
  • Adjoint functors in category theory
  • Hermitian adjoint (adjoint of a linear operator) in functional analysis
  • Adjoint representation of a Lie group
  • 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
  • For the adjoint of a differential operator with general polynomial coefficients see differential operator