adjoints background

adjoints

/ˈædʒɔɪnts/

Illustration adjoints - Image 1

noun

伴随矩阵， adj矩阵

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. "

为了求伴随矩阵（adj矩阵），我们首先计算了原矩阵的各个代数余子式，然后求了转置。

Illustration adjoints - Image 1

noun

伴随矩阵，厄米转置矩阵。

(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. "

代表学生数学和科学成绩的矩阵的伴随矩阵帮助老师计算了每个科目的平均表现。

Illustration adjoints - Image 1

noun

伴随算子，厄米共轭

(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. "

在量子力学中，物理学家经常使用“伴随算子”这个术语来指代互为厄米共轭的算符，因为这些算符在描述可观测量方面起着关键作用。

Illustration adjoints - Image 1

noun

伴随，伴随函子。

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. "

在高等数学中，函子之间可以存在关联，我们经常会讨论一个函子和它的伴随函子。

Illustration adjoints - Image 1

noun

伴随曲线

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." "

在研究代数曲线时，数学家经常分析伴随曲线，以便理解原始曲线上那些奇异点，也就是多重数很高的点。

Illustration adjoints - Image 1

noun

副官，助理。

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. "

那位将军有几位副官，帮助他处理日常事务和信件。

military government position job

Illustration adjoints - Image 1

noun

副市长, 助理市长

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. "

在这个法国小镇里，镇长非常依赖他的副市长们管理各项社区服务，从组织每周的集市到监督当地学校，事无巨细。

politics government