Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. used in several situations with a meaning similar to helping
 n. A matrix in which each element is the cofactor of an associated element of another matrix.
 n. An assistant mayor of a French commune
from the GNU version of the Collaborative International Dictionary of English
 n. An adjunct; a helper.
from The Century Dictionary and Cyclopedia
 n. 1. One who is joined or associated with another as a helper; an adjunct.
 n. In France, specifically — An assistant of or substitute for the mayor of a commune, or in Paris of an arrondissement. An assistant professor in a college.
Etymologies
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Examples

His adjoint was the Colonel Comte de Mazancourt, his aidedecamp

_Combat_, signed by the "adjoint" of the 13th arrondissement.

The parameter Lambda of gauge transformation in this threealgebra realm have two "adjoint" indices instead of one.

It is as though every Idea has two faces, which are like love and anger: love in search of the fragments, the progressive determination and linking of the ideal adjoint fields; anger in the condensation of singularities which, by dint of ideal events, defines the concentration of a "revolutionary situation" and causes the Idea to explode into the actual.
Notes on 'Repetition, Representation and Revolution: Deleuze and Blake's _America_'

There remains to recover, e.g., the representation of “observables” by selfadjoint operators, and the dynamics (unitary evolution).

It is not difficult to show that a selfadjoint operator P with spectrum contained in the twopoint set {0,1} must be a projection; i.e.,

Each bounded simple random variable f gives rise to a bounded selfadjoint operator A =

Studying the properties off these observations one sees that they satisfy the necessary axioms to be linear operators, and, in fact, selfadjoint operators.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

Controls on ocean productivity and airsea carbon flux: An adjoint model sensitivity study.

Pauli pointed out that a (selfadjoint) time operator is incompatible with a Hamiltonian spectrum bounded below.
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