Adjoint

Part of speech: adjective, noun

Pronunciation: /ˈæd͡ʒ.ɔɪnt/

Definitions

1. A mathematical term describing a concept related to an original structure that usually applies to transformations of linear equations
2. In mathematics, it refers to an operation associated with matrices that facilitates relation among transformations
3. Refers to a mathematical concept describing an operator closely associated with another to reflect symmetry or duality ; denotes a matrix-related operation that produces a corresponding counterpart used in solving linear systems

Etymology: The word comes from French "adjoindre," meaning "to join," which entered English as "adjoin." Its close relative "adjunct" arrived from the same Latin source by a separate route, which makes the two a doublet: one came through French and the other was taken more directly from Latin, so they share a root but developed different senses. In mathematics, "adjoint" describes a partner operator or function that is linked to an original structure, most commonly in the study of linear transformations, where it pairs with the original in a way that mirrors how one object joins another. The mathematical sense has a tangled history. In category theory, which draws together ideas from many fields, the term is often mixed up with "adjunct," and the pairing of two such functors is called an "adjunction." Because of this overlap, the origin of any particular mathematical usage can be hard to pin down, and different branches of mathematics adopted the word at different points.

Synonyms: adjunct, associated, related

Antonyms: independent, detached