[{"word":"adjoint","phonetic":"/ˈædʒ.ɔɪnt/","phonetics":[{"text":"/ˈædʒ.ɔɪnt/","audio":""}],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"The transpose of the cofactor matrix of a given square matrix.","synonyms":[],"antonyms":[]},{"definition":"(of a matrix) Transpose conjugate.","synonyms":[],"antonyms":[]},{"definition":"(of an operator) Hermitian conjugate.","synonyms":[],"antonyms":[]},{"definition":"A functor related to another functor by an adjunction.","synonyms":[],"antonyms":[]},{"definition":"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.","synonyms":[],"antonyms":[]},{"definition":"An assistant to someone who holds a position in the military or civil service.","synonyms":[],"antonyms":[]},{"definition":"An assistant mayor of a French commune.","synonyms":[],"antonyms":[]}],"synonyms":[],"antonyms":[]},{"partOfSpeech":"adjective","definitions":[{"definition":"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).","synonyms":[],"antonyms":[]},{"definition":"(of a functor) That is related to another functor by an adjunction.","synonyms":[],"antonyms":[]},{"definition":"(of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.","synonyms":[],"antonyms":[]}],"synonyms":["adjunct"],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/adjoint"]}]