adjoint

简明释义

英[ˈædˌdʒɔɪnt]美[əˈdʒɔɪnt]

n. 伴随矩阵

adj. 伴随的

英英释义

单词用法

同义词

反义词

例句

1.The decomposition technology for establishing adjoint equations is put forward.

提出了建立伴随方程的分解技术；

2.Since the characteristic of its coefficient, adjoint polynomials'roots has some specific property.

由于伴随多项式系数的特点，决定了它的根具有特殊性。

3.The adjoint coefficient of sound radiation modes is proportional to the corresponding sound radiation power.

声辐射模态伴随系数与对应的辐射声功率成正比。

4.In this paper the idea of synchronous vector and adjoint matrix are proposed.

本文提出了同步矢量和伴生矩阵的概念。

5.It is important in ASAC based on acoustic radiation modes to obtain adjoint coefficients of the radiation modes.

声辐射模态伴随系数的获取是基于声辐射模态理论进行ASAC控制中的重要环节。

6.The time to integrate adjoint equations can be shortened.

反向积分伴随方程的时间可以缩短。

7.In the end we prove that idempotent operator is similar to its adjoint.

最后还证明了幂等算子和它的伴随是相似的。

8.The example of a numerical prediction model shows the basic method of developing adjoint assimilation system of numeric predict model.

而后以一个数值预报模式为例，说明了构造伴随模式同化系统的基本方法。

9.An expression of the generalized eigenvector of adjoint matrices for nonsingular matrix a is derived.

给出了非奇异矩阵a的伴随的广义特征向量的表达式。

10.The professor appointed an adjoint 副教授 to assist with the research project.

教授任命了一位adjoint 副教授来协助研究项目。

11.In mathematics, the adjoint 伴随算子 of a linear operator plays a crucial role in functional analysis.

在数学中，线性算子的adjoint 伴随算子在泛函分析中起着至关重要的作用。

12.She worked as an adjoint 助理 to the director of the film.

她担任电影导演的adjoint 助理。

13.The adjoint 副职 manager was responsible for overseeing daily operations.

这位adjoint 副职经理负责监督日常运营。

14.In quantum mechanics, the adjoint 伴随态 of a state vector is essential for calculating probabilities.

在量子力学中，状态向量的adjoint 伴随态对计算概率至关重要。

作文

In the realm of mathematics and physics, the term adjoint (伴随) plays a crucial role in various theories and applications. The concept of an adjoint operator is fundamental in linear algebra, particularly in the study of inner product spaces. An adjoint operator is defined as a linear transformation that is closely related to another linear transformation, often providing essential insights into the properties of the original operator. Understanding the nature of adjoint operators allows mathematicians and physicists to explore deeper relationships within their respective fields. For example, consider a linear operator represented by a matrix. The adjoint of this matrix, also known as the conjugate transpose, is obtained by taking the transpose of the matrix and then taking the complex conjugate of each element. This operation is critical when dealing with quantum mechanics, where adjoint operators are used to describe observable quantities. In quantum mechanics, the adjoint of an operator corresponds to the physical observables we can measure, making it a vital component in understanding the behavior of quantum systems. Moreover, in functional analysis, the concept of adjoint extends beyond finite-dimensional spaces to infinite-dimensional Hilbert spaces. Here, the adjoint operator preserves the structure of the space and ensures that certain properties hold true. For instance, if an operator is self-adjoint, it means that it is equal to its own adjoint, which has significant implications for the eigenvalues and eigenvectors of the operator. Self-adjoint operators have real eigenvalues, which is a desirable property in many physical applications. The importance of adjoint operators also extends to numerical methods, particularly in optimization problems. In optimization, the adjoint method is often employed to efficiently compute gradients of functions, which is essential for finding optimal solutions. By utilizing the adjoint approach, one can reduce computational costs significantly while maintaining accuracy in the results. This technique is prevalent in various fields, including machine learning, control theory, and engineering. Furthermore, the concept of adjoint is not limited to mathematics alone; it has profound implications in computer science, particularly in programming languages and algorithms. Some programming paradigms utilize adjoint concepts to create more efficient algorithms that can handle complex data structures. Understanding how adjoint relationships work can lead to better algorithm design and implementation, ultimately improving performance and reducing resource consumption. In conclusion, the term adjoint (伴随) encompasses a wide range of applications across various disciplines, including mathematics, physics, optimization, and computer science. Its significance cannot be overstated, as it provides essential insights into the structure and behavior of linear transformations and their associated properties. As we delve deeper into the intricacies of these fields, the understanding of adjoint operators and their applications will undoubtedly continue to evolve, paving the way for new discoveries and advancements in science and technology.

在数学和物理的领域中，术语adjoint（伴随）在各种理论和应用中扮演着至关重要的角色。adjoint算子的概念在线性代数中是基础，尤其是在内积空间的研究中。adjoint算子被定义为与另一个线性变换密切相关的线性变换，通常为原始算子的性质提供重要的见解。理解adjoint算子的性质使得数学家和物理学家能够深入探索各自领域内的更深层次的关系。 例如，考虑一个由矩阵表示的线性算子。这个矩阵的adjoint，也称为共轭转置，是通过对矩阵进行转置，然后对每个元素取复共轭来获得的。这一操作在处理量子力学时至关重要，其中adjoint算子用于描述可观测量。在量子力学中，一个算子的adjoint对应于我们可以测量的物理可观测量，使其成为理解量子系统行为的重要组成部分。 此外，在泛函分析中，adjoint的概念超越了有限维空间，扩展到无限维希尔伯特空间。在这里，adjoint算子保持空间的结构，并确保某些性质成立。例如，如果一个算子是自伴随的，这意味着它等于其自身的adjoint，这对算子的特征值和特征向量具有重要意义。自伴随算子具有实特征值，这是许多物理应用中所期望的属性。 adjoint算子的意义还扩展到数值方法，特别是在优化问题中。在优化中，adjoint方法通常被用来有效计算函数的梯度，这对于寻找最优解至关重要。通过利用adjoint方法，可以显著降低计算成本，同时保持结果的准确性。这种技术在机器学习、控制理论和工程等多个领域中普遍存在。 此外，adjoint的概念不仅限于数学；它在计算机科学中也有深远的影响，特别是在编程语言和算法方面。一些编程范式利用adjoint概念来创建更高效的算法，以处理复杂的数据结构。理解adjoint关系的工作原理可以导致更好的算法设计和实现，最终提高性能并减少资源消耗。 总之，术语adjoint（伴随）涵盖了各个学科中的广泛应用，包括数学、物理、优化和计算机科学。它的重要性不容小觑，因为它为线性变换及其相关属性的结构和行为提供了基本见解。当我们深入探讨这些领域的复杂性时，对adjoint算子及其应用的理解无疑将继续发展，为科学和技术的新发现和进步铺平道路。