Background for adjoints

adjoints

/ˈædʒɔɪnts/

Illustration adjoints - Image 1

noun

The transpose of the cofactor matrix of a given square matrix.

Examples :

"To find the adjoints, we first calculated the cofactors of the original matrix and then took the transpose. "

Illustration adjoints - Image 1

noun

(of a matrix) Transpose conjugate.

Examples :

"The adjoints of the matrix representing student scores in math and science classes helped the teacher calculate the average performance in each subject. "

Illustration adjoints - Image 1

noun

(of an operator) Hermitian conjugate.

Examples :

"In quantum mechanics, physicists often use the term "adjoints" to refer to operators that are Hermitian conjugates of each other, as these operators play key roles in describing observable quantities. "

Illustration adjoints - Image 1

noun

A functor related to another functor by an adjunction.

Examples :

"In advanced mathematics, functors can be related, and we often talk about one functor and its adjoints. "

Illustration adjoints - Image 1

noun

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.

Examples :

""When studying algebraic curves, mathematicians often analyze adjoints to understand the singularities, or points of high multiplicity, on the original curve." "

Illustration adjoints - Image 1

noun

An assistant to someone who holds a position in the military or civil service.

Examples :

"The general had several adjoints who helped him manage his daily schedule and correspondence. "

military government position job

Illustration adjoints - Image 1

noun

An assistant mayor of a French commune.

Examples :

"In the small French town, the mayor relied heavily on his adjoints to manage the various community services, from organizing the weekly market to overseeing the local school. "

politics government