adjoint

What it means

1. not comparablemathematicsUsed 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 comparablecategory theoryThat is related to another functor by an adjunction.
3. not comparablegeometryHaving a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.

   This imposes n(n - 3)/2 conditions on the n-gon adjoint curve.

   2016, Eugene Wachspress, Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics, page 216

   2 more 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.

   1933, H. F. Baker, Principles of Geometry, volume 5, published 2010, page 103

   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.

   1963, Julian Lowell Coolidge, A History of Geometrical Methods, page 205

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.

1933, H. F. Baker, Principles of Geometry, volume 5, published 2010, page 103

Where it comes from

1. Frenchadjoindre“to join”
2. Englishadjoint

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.