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:
- 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.