a generalization in category theory of this notion
adjoint in American English
(ˈædʒɔint)
noun Math
1.
a square matrix obtained from a given square matrix and having the property that its product withthe given matrix is equal to the determinant of the given matrix times the identity matrix
2. Also called: Hermitian conjugate, transposed conjugate
the matrix obtained from a given matrix by interchanging rows and columns and by replacing each element by its complex conjugate
Word origin
[ad- + joint]ad- is a prefix occurring in loanwords from Latin, where it meant “toward” and indicateddirection, tendency, or addition (adjoin)
Examples of 'adjoint' in a sentence
adjoint
Every conformal field theory has the symmetry of taking each field to its adjoint.
Doron Gepner, Hervé Partouche 2018, 'On the Real Part of a Conformal Field Theory', Universehttp://www.mdpi.com/2218-1997/4/9/97. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Two methods for the eigen-mode adjoint flux calculation were implemented.
Jin Young Cho, Tae Young Han, Ho Jin Park, Ser Gi Hong, Hyun Chul Lee 2019, 'Improvement and verification of the DeCART code for HTGR core physics analysis', Nuclear Engineering and Technologyhttp://www.sciencedirect.com/science/article/pii/S1738573318302493. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Using a gradient check, the correctness of the adjoint model was verified.
Yaodeng Chen, Ruizhi Zhang, Yufang Gao, Changna Lu 2014, 'Analysis of the Properties of Adjoint Equations and Accuracy Verification of AdjointModel Based on FVM', Abstract and Applied Analysishttp://dx.doi.org/10.1155/2014/407468. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This paper presents and compares methodologies to generate discrete adjoint codes.
Christèle Faure, Isabelle Charpentier 2001, 'Comparing Global Strategies for Coding Adjoints', Scientific Programminghttp://dx.doi.org/10.1155/2001/485915. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We show that the adjoint factorization corresponds precisely to the complex splitting.
F. M. Mahomed, A. Qadir, A. Ramnarain 2011, 'Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by ComplexMethods', Mathematical Problems in Engineeringhttp://dx.doi.org/10.1155/2011/202973. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)