adjoint background

adjoint

/ˈædʒ.ɔɪnt/

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noun

伴随矩阵，adjugate 矩阵。

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

Examples :

"To find the inverse of a matrix, you first calculate the adjoint. "

要计算一个矩阵的逆矩阵，你首先要计算它的伴随矩阵 (bànsuí jǔzhèn)。

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noun

伴随矩阵，厄米转置矩阵

(of a matrix) Transpose conjugate.

Examples :

"The adjoint of the matrix representing the students' test scores is used to calculate the average score for each subject. "

代表学生考试成绩的矩阵的伴随矩阵(厄米转置矩阵)被用来计算每个科目的平均分数。

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noun

伴随，厄米共轭。

(of an operator) Hermitian conjugate.

Examples :

"In quantum mechanics, the adjoint of an operator describes how it acts on the "conjugate" state of a quantum system. "

在量子力学中，一个算符的伴随算符（厄米共轭）描述了该算符如何作用于量子系统的“共轭”态。

math physics technical

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noun

伴随，伴随函子

A functor related to another functor by an adjunction.

Examples :

""In advanced mathematics, understanding a functor often requires examining its adjoint, a related functor that helps explain its behavior." "

在高等数学中，理解一个函子通常需要考察它的伴随函子，这个相关的函子能帮助解释它的行为。

Illustration adjoint - Image 1

noun

伴随曲线，副曲线。

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 :

"The professor explained that to fully understand the complex curve, we also needed to examine its adjoint. "

为了完全理解这条复杂的曲线，教授解释说我们还需要研究它的伴随曲线/副曲线 (bàn suí qū xiàn / fù qū xiàn)。

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noun

副官，助手。

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

Examples :

"The general's adjoint handled all the logistics for the upcoming troop deployment. "

那位将军的副官负责处理即将到来的部队部署的所有后勤事宜。

military government position job

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noun

副市长

An assistant mayor of a French commune.

Examples :

"The adjoint helped the mayor of the small French town organize the annual Bastille Day celebration. "

这位副市长协助这个法国小镇的市长组织了一年一度的法国国庆日庆祝活动。

politics government

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adjective

伴随的，毗连的。

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).

Examples :

"In her linear algebra class, the professor explained the adjoint operator, clarifying how it helps to find the "conjugate transpose" of a matrix, which is like a reflection of the matrix combined with a form of conjugation. "

在线性代数课上，教授讲解了伴随算子，并解释了它如何帮助找到矩阵的“共轭转置”，这就像矩阵的镜像反射与一种共轭形式的结合。

math technical science logic system

Illustration adjoint - Image 1

adjective

伴随的, 毗连的.

(of a functor) That is related to another functor by an adjunction.

Examples :

"The left-hand adjoint functor in our linear algebra class is closely related to the right-hand functor used to solve systems of equations. "

在线性代数课中，我们学到的左伴随函子和用来解方程组的右函子密切相关。

math technical logic

Illustration adjoint - Image 1

adjective

相伴的，伴随的

(of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.

Examples :

"The second curve was adjoint, sharing three crucial points with the original design. "

第二条曲线是相伴的，它与最初的设计共享了三个关键点。