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 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

Other articles related to "adjoint":

Closed Operator - Adjoint
... The adjoint of an unbounded operator can be defined in two equivalent ways ... it can be defined in a way analogous to how we define the adjoint of a bounded operator ... Namely, the adjoint T∗ H2 → H1 of T is defined as an operator with the property More precisely, T∗ is defined in the following way ...
La Goutelle - Administration
... The mayor is Jean BOUCHERET, 1nd Adjoint Maurice MARTIN, 2rd Adjoint Jean-Francois MARCHEIX and 3rd Adjoint Stephane NEBUS ... The Maire-Adjoint, Michel BONNAFOUX, resigned in somewhat acrimonious circustances in 2009 ...
Tensor-hom Adjunction
... adjunction is that the tensor product and Hom functors and form an adjoint pair This is made more precise below ... The order "tensor-hom adjunction" is because tensor is the left adjoint, while hom is the right adjoint ...
Multipliers And Centralizers (Banach Spaces) - Definitions
... to be a multiplier if every point p in Ext(X) is an eigenvector for the adjoint operator T∗ X∗ → X∗ ... a function aT Ext(X) → K such that Given two multipliers S and T on X, S is said to be an adjoint for T if i.e ... of X, denoted Z(X), is the set of all multipliers on X for which an adjoint exists ...