What does "adjoint" mean?
The transpose of the cofactor matrix of a given square matrix.
Adjoint
/ˈæd͡ʒ.ɔɪnt/ adj, noun
adj, noun ·Rare ·Advanced level
Meaning at a glance
- Primary sense: The transpose of the cofactor matrix of a given square matrix.
- Grammar: adjoint is listed as adj, noun.
- Nearest alternatives: adjunct, dagger.
- Usage evidence: 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.
How to use "adjoint"
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Source and review context
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Definitions
Noun
- 1 The transpose of the cofactor matrix of a given square matrix.
- 2 Transpose conjugate.
- 3 Hermitian conjugate.
- 4 A functor related to another functor by an adjunction.
- 5 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.
Show 2 more definitions
- 6 An assistant to someone who holds a position in the military or civil service.
". 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."
- 7 An assistant mayor of a French commune.
"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."
Adjective
- 1 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). not-comparable
- 2 That is related to another functor by an adjunction. not-comparable
- 3 Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with. not-comparable
"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."
Synonyms
All synonymsExample
"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."
Common questions
What is a synonym for "adjoint"?
Common synonyms include: adjunct, dagger.
How do you use "adjoint" in a sentence?
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.
How do you pronounce "adjoint"?
Pronounced /ˈæd͡ʒ.ɔɪnt/.
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.