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 they type

(Ax,y) = [x, By].

Specifically:

• the adjoint of an operator in functional analysis
  • see differential operator for the adjoint of a differential operator with general polynomial coefficients
  • the adjoint or conjugate transpose of a matrix in linear algebra;
• the left adjoint or right adjoint in a pair of adjoint functors, in category theory;
  • the upper and lower adjoints of a Galois connection in order theory;
• the adjoint representation of a Lie group;
• an adjoint curve, in the traditional treatment of coherent duality for a linear system of curves.
• the classical adjoint or adjugate of a matrix, related to its inverse.