Definitions
from The Century Dictionary.
 noun 1. One who is joined or associated with another as a helper; an adjunct.
 noun 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.
from the GNU version of the Collaborative International Dictionary of English.
 noun obsolete An adjunct; a helper.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics used in several situations with a meaning similar to
helping  noun mathematics A
matrix in which eachelement is thecofactor of an associated element of another matrix.  noun An
assistant mayor of a Frenchcommune
Etymologies
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Examples

His adjoint was the Colonel Comte de Mazancourt, his aidedecamp
The Diary and Letters of Madame D'Arblay — Volume 3 Fanny Burney 1796

_Combat_, signed by the "adjoint" of the 13th arrondissement.
Diary of the Besieged Resident in Paris Henry Labouchere 1871

The parameter Lambda of gauge transformation in this threealgebra realm have two "adjoint" indices instead of one.
The Reference Frame 2010

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_' 2008

There remains to recover, e.g., the representation of “observables” by selfadjoint operators, and the dynamics (unitary evolution).
Puppet X: 1 2009

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.,
Puppet X: 1 2009

Each bounded simple random variable f gives rise to a bounded selfadjoint operator A =
Puppet X: 1 2009

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 Sean 2008

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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