adjoint
Part of speech: adj
noun
Morphological type: simple
Topics: algebraic-geometry
category-theory
computing
engineering
geometry
linear-algebra
mathematical-analysis
mathematics
natural-sciences
physical-sciences
sciences
Etymology: From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct.
In the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.
Inflected forms:
form: adjoints
pos: noun
tags: plural
Senses:
gloss: Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation).
pos: adj
tags: not-comparable
gloss: That is related to another functor by an adjunction.
pos: adj
tags: not-comparable
gloss: Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.
pos: adj
tags: not-comparable
examples: The sets A + A₀, B + B₀, together, form the complete intersection, with f = 0, of a composite adjoint curve of order m + k, consisting of the adjoint curve of order m through A + B, together with the non-adjoint curve ω = 0; and the set B + B₀ consists of p points, and lies on i + j adjoint φ-curves of f = 0.
As we have stated before, a curve f' is adjoint to a curve f if it have at least the multiplicity r#95;i-1 at each point where f has the multiplicity r#95;i. A first polar #92;sum#95;iy#95;i#92;left(#92;partialf#47;#92;partialx#95;i#92;right)#61;0 is an example of an adjoint curve.
This imposes n(n - 3)/2 conditions on the n-gon adjoint curve.
gloss: The transpose of the cofactor matrix of a given square matrix.
pos: noun
gloss: Transpose conjugate.
pos: noun
gloss: Hermitian conjugate.
pos: noun
gloss: A functor related to another functor by an adjunction.
pos: noun
gloss: A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.
pos: noun
gloss: An assistant to someone who holds a position in the military or civil service.
pos: noun
examples: . Nominated the citizens Fayolles, captain of infantry, and Favery of the Engineers to be my adjoints, and dispatched the letters of nomination to the Minister at War, so now I am fairly afloat.
Even as it is, by the reckless aggregation of machine-workers and their adjoints in the great cities and the manufacturing districts, it has kept down life amongst us, and keeps it down to a miserably low standard; so low that any standpoint for improvement is hard to think of even.
The chef and his adjoints are seen by this code as part of the military, subject to military jurisdiction despite their obligation to execute the orders of the administrative council and of the justice of the peace.
gloss: An assistant mayor of a French commune.
pos: noun
examples: A vigorous, aggressive, and ambitious mayor will not rely overmuch upon his adjoints, but a mayor of the more passive type will lean heavily upon them.
Mayors and their adjoints were often simple cultivateurs like the majority of the community.
Synonyms: adjunct
Related words: adjunction
coadjoint
self-adjoint
sub-adjoint
Derived words: adjointable
adjoint action
adjoint curve
adjoint endomorphism
adjoint functor
adjointly
adjoint matrix
adjointness
adjoint operator
adjoint representation
left adjoint functor
nonadjoint
right adjoint functor
biadjoint
sub-adjoint
Translations:
lang: Bulgarian
word: спрегнат
roman: spregnat
lang: Esperanto
word: adjunkta
lang: German
word: adjungiert
lang: Spanish
word: adjunta