orthogonality

简明释义

英[ˌɔrθəˈɡɒnəlɪti]美[ˌɔrθəˈɡɒnəlɪti]

n. [数] 正交性；相互垂直

英英释义

单词用法

同义词

反义词

例句

1.Derived the orthogonality of the beam-column structure when the material of beam different from the material of column in structure.

针对此类梁-柱结构推导了梁和柱的材料不同时的正交性条件。

2.Based on the orthogonality of rotation matrix, a constrained optimization approach is proposed to estimate the rotation matrix.

本文利用旋转矩阵的正交性，提出了进一步改善原旋转矩阵估计的约束优化方法。

3.Is Orthogonality inversely proportional with DRY principles?

正交性成反比与干的原则？

4.The results prove that this plan not only ensures the rotating matrix 's orthogonality but also improves the calibrating precision.

结果表明，该方案不仅保证了旋转矩阵的正交性，同时提高了定标精度。

5.Orthogonality of system architecture can be reduced by performing one-to-one functional mapping.

正交性的缺点可以通过减少系统架构一对一映射功能的方式得到改善。

6.Due to orthogonality property, the coefficient in each term of either series can be expressed in a linear function of the coefficients of the other series.

利用级数的正交性质，其中任一级数中的每项系数都可表达为另一级数的各项系数的线性函数。

7.Discussion is made about the orthogonality conditions of the modal functions.

并对模态函数的正交性作了相关探讨。

8.It can ensure unitary column orthogonality for the resulting matrix sequence.

该方法可确保迭代矩阵列的单位列正交性。

9.In statistics, the concept of orthogonality is crucial for ensuring that different variables do not interfere with each other, allowing for clearer analysis.

在统计学中，正交性的概念对于确保不同变量之间不相互干扰至关重要，从而允许更清晰的分析。

10.In programming, using orthogonality in language design means that features can be combined without unexpected interactions.

在编程中，语言设计中的正交性意味着特性可以组合而不会产生意外的交互。

11.The orthogonality of the two functions allows us to treat them independently when solving the equation.

这两个函数的正交性使我们在求解方程时可以独立对待它们。

12.In linear algebra, the orthogonality of vectors simplifies many calculations and helps in understanding vector spaces.

在线性代数中，向量的正交性简化了许多计算，并有助于理解向量空间。

13.The orthogonality principle in signal processing helps to separate signals without interference.

信号处理中的正交性原理有助于在没有干扰的情况下分离信号。

作文

In the realm of mathematics and computer science, the concept of orthogonality plays a crucial role in understanding various systems and processes. At its core, orthogonality refers to the idea of independence or non-interference among components. When two elements are said to be orthogonal, it means that they do not influence each other, and changes in one will not affect the other. This principle is not only applicable in theoretical frameworks but also has practical implications in fields such as engineering, programming, and even economics. To illustrate the importance of orthogonality, consider the design of software systems. In programming, achieving orthogonality among different modules can lead to more maintainable and scalable code. For instance, if a software application is built with well-defined modules that operate independently, developers can modify one module without worrying about unintended consequences in others. This independence enhances the overall robustness of the system, making it easier to debug and extend. Moreover, orthogonality is a key principle in linear algebra, where it describes the relationship between vectors. Two vectors are orthogonal if their dot product equals zero, indicating that they are at right angles to each other in a multi-dimensional space. This geometric interpretation helps in various applications, such as optimizing solutions in machine learning algorithms, where orthogonal features can lead to better model performance. By ensuring that features do not overlap, we can create models that generalize well to new data. In addition to mathematics and programming, orthogonality can also be observed in the realm of communication. In signal processing, for example, orthogonal signals can coexist without interference, allowing for more efficient use of bandwidth. This principle is fundamental in technologies such as Orthogonal Frequency Division Multiplexing (OFDM), which is widely used in modern wireless communications. By transmitting multiple signals simultaneously without interference, OFDM maximizes the capacity of communication channels. Furthermore, the concept of orthogonality extends beyond technical disciplines into the social sciences. In decision-making processes, orthogonal factors can help analyze complex problems by breaking them down into independent components. For instance, when evaluating a business strategy, one can consider factors such as market trends, consumer behavior, and financial implications separately. This approach allows for a clearer understanding of each factor's impact, leading to more informed decisions. In conclusion, orthogonality is a multifaceted concept that transcends various domains, from mathematics to engineering and beyond. Its emphasis on independence and non-interference among components not only simplifies complex systems but also enhances their efficiency and effectiveness. By embracing the principles of orthogonality, we can foster innovation and improvement across diverse fields, ultimately leading to better outcomes and advancements in technology and society. Understanding this concept is essential for anyone looking to navigate the complexities of modern systems, whether in academia, industry, or everyday life.

在数学和计算机科学领域，正交性的概念在理解各种系统和过程方面发挥着至关重要的作用。从本质上讲，正交性指的是组件之间独立或不干扰的思想。当两个元素被称为正交时，这意味着它们不会相互影响，一个的变化不会影响另一个。这一原则不仅适用于理论框架，而且在工程、编程甚至经济学等领域具有实际意义。 为了说明正交性的重要性，可以考虑软件系统的设计。在编程中，实现不同模块之间的正交性可以导致更易维护和可扩展的代码。例如，如果一个软件应用程序是由定义良好的独立模块构建的，开发人员可以修改一个模块，而不必担心对其他模块产生意外后果。这种独立性增强了系统的整体健壮性，使调试和扩展变得更加容易。 此外，正交性是线性代数中的一个关键原则，它描述了向量之间的关系。如果两个向量的点积等于零，则它们是正交的，这表明它们在多维空间中彼此成直角。这种几何解释在各种应用中都很有帮助，例如在机器学习算法中优化解决方案，其中正交的特征可以导致更好的模型性能。通过确保特征不重叠，我们可以创建能够很好地推广到新数据的模型。 除了数学和编程，正交性还可以在通信领域观察到。例如，在信号处理过程中，正交的信号可以共存而不干扰，从而允许更有效地利用带宽。这个原则在现代无线通信技术中是基础，如正交频分复用（OFDM），它广泛应用于现代无线通信中。通过同时传输多个信号而不干扰，OFDM最大化了通信通道的容量。 此外，正交性的概念超越了技术学科，延伸到了社会科学。在决策过程中，正交的因素可以通过将复杂问题分解为独立组件来帮助分析。例如，在评估商业战略时，可以分别考虑市场趋势、消费者行为和财务影响等因素。这种方法使每个因素的影响更清晰，从而导致更明智的决策。 总之，正交性是一个多面的概念，跨越多个领域，从数学到工程及其他领域。它强调组件之间的独立性和非干扰性，不仅简化了复杂系统，还增强了其效率和有效性。通过接受正交性的原则，我们可以促进各个领域的创新和改进，最终导致技术和社会的更好结果和进步。理解这一概念对于任何希望驾驭现代系统复杂性的人来说都是至关重要的，无论是在学术界、工业界还是日常生活中。