adjoint

adjective

1. not comparable 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).
2. not comparable, of a functor That is related to another functor by an adjunction.
3. not comparable, of one curve to another curve Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with. 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

Similar: adjunct

noun adjoints

1. The transpose of the cofactor matrix of a given square matrix.
2. of a matrix Transpose conjugate.
3. of an operator 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.
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.