Adjoint

From Wikipedia, the free encyclopedia

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 may mean:

• Adjoint of an operator, in functional analysis
• Adjoint functors, in category theory
• Adjoint representation of a Lie group
• Adjoint endomorphism of a Lie algebra
• Adjoint curve, in the traditional treatment of coherent duality for a linear system of curves
• Conjugate transpose of a matrix in linear algebra
• Adjugate of a matrix, related to its inverse.
• 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