---
title: "Adjoint"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Adjoint"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T07:22:59.225743+00:00"
instance: "kb-cron"
---

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 of a linear map, also called its transpose in case of matrices
Hermitian adjoint (adjoint of a linear operator) in functional analysis
Adjoint endomorphism of a Lie algebra
Adjoint representation of a Lie group
Adjoint functors in category theory
Adjunction (field theory)
Adjunction formula (algebraic geometry)
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
The adjoint of a differential operator with general polynomial coefficients
Kleisli adjunction
Monoidal adjunction
Quillen adjunction
Axiom of adjunction in set theory
Adjunction (rule of inference)