orthonormal

简明释义

英[/ˌɔrθoʊˈnɔrməl/]美[/ˌɔrθoʊˈnɔrməl/]

adj. [数] 标准正交的；正规化的；[数] 规格化正交的

英英释义

单词用法

同义词

反义词

例句

1.A filter based on orthonormal wavelet bases is designed to do wavelet transform with images. Different scale image edges can be detected form different scale image wavelet transform.

基于正交二进小波，设计了一个滤波器对图象进行多尺度滤波，得到不同尺度的小波变换。

2.From this, detection, location and classification of power quality's disturbances are analyzed respectively, by the symmetry complex compactly-supported orthonormal wavelet constructed.

利用所构造的复数正交紧支对称小波，分别研究了电网电能质量扰动的检测、定位与分类问题。

3.Aiming at the security and credibility requirement of power protection equipment, power spectrum estimate algorithm which based on multiple orthonormal tapers is researched and modified in this paper.

针对电力保护设备的安全性和可信赖性指标要求，研究了基于多正交窗分析的功率谱估计算法，并从计算量的角度出发对算法进行了改进。

4.Because the algorithm optimized the rotation angles directly, the orthonormal constraints were easily satisfied in the present method.

由于该算法直接优化摄像机的旋转角度，所以本文的标定方案能够容易地满足旋转矩阵正交约束条件。

5.According to the need of our project, the parallel implementation of QR orthonormal transform is also been discussed in this paper.

根据课题需要，本文对QR正交变换的并行实现也进行了探讨。

6.By extending the theory of multi-resolution analysis to multi-bank wavelets, this paper also focuses on the study of 4-bank compactly supported bi-symmetric orthonormal wavelets.

通过将多分辨分析扩展到多进小波的办法，本文也构造了一个具有双对称性、紧支撑集和高阶消失矩的4-进正交小波类。

7.This result shows that if we want to construct orthonormal wavelets from a multireso- lotion, then that multiresolution must have an orthonormal scaling function.

结果表明，如果我们想从多尺度分析出发构造正交小波，那么该多尺度分析必须有正交尺度函数。

8.One kind of Modified Orthonormal Finite Ridgelet Transform was brought forward.

提出了一种改进型正交有限脊波分析的图像去噪算法。

9.In an orthographic projection, also called "orthonormal", on the other hand, you have a viewing direction but not a viewing point o.

另一方面，在所谓垂直投影(也叫规格化正交投影)中，你是从一个方向上进行观察，而不是一个观察点。

10.In linear algebra, a set of vectors is called orthonormal 正交规范的 if they are all unit vectors and mutually perpendicular.

在线性代数中，如果一组向量都是单位向量并且相互垂直，则称这组向量为orthonormal 正交规范的。

11.An orthonormal 正交规范的 basis simplifies many calculations in quantum mechanics.

在量子力学中，orthonormal 正交规范的 基础简化了许多计算。

12.The Fourier transform uses orthonormal 正交规范的 functions to represent signals in frequency space.

傅里叶变换使用orthonormal 正交规范的 函数来表示频域中的信号。

13.When performing PCA, it is important to ensure that the resulting components are orthonormal 正交规范的.

在进行主成分分析时，确保结果组件是orthonormal 正交规范的 是很重要的。

14.In computer graphics, orthonormal 正交规范的 coordinate systems help with transformations and rendering.

在计算机图形学中，orthonormal 正交规范的 坐标系统有助于转换和渲染。

作文

In the field of mathematics and physics, the concept of orthonormal vectors plays a crucial role in various applications, particularly in linear algebra and functional analysis. To understand what orthonormal means, we first need to break it down into its components. The term 'orthogonal' refers to vectors that are perpendicular to each other, while 'normal' indicates that these vectors have a unit length, or magnitude equal to one. Therefore, a set of vectors is considered orthonormal if they are both orthogonal and normalized. The significance of orthonormal vectors can be seen in numerous mathematical contexts. For instance, in the realm of Euclidean space, any two-dimensional vector can be expressed as a linear combination of two orthonormal basis vectors. This simplification allows for easier calculations and clearer geometric interpretations. When vectors are orthonormal, the computations involving dot products become straightforward, as the dot product of any two different orthonormal vectors equals zero, while the dot product of a vector with itself equals one. An example of orthonormal vectors can be found in the standard basis of ℝ^n, where the vectors e1 = (1, 0), e2 = (0, 1), and so forth, are all orthonormal. These basis vectors not only represent directions in space but also serve as a foundation for constructing other vectors in that space. By expressing any vector as a combination of these orthonormal basis vectors, one can simplify many operations such as projections and transformations. In addition to their mathematical elegance, orthonormal vectors have practical applications in various fields such as computer graphics, quantum mechanics, and signal processing. In computer graphics, orthonormal bases are used to define coordinate systems that make rendering images more efficient. In quantum mechanics, the states of a quantum system can be represented using orthonormal vectors in a Hilbert space, which allows physicists to calculate probabilities and expectations accurately. Moreover, the concept of orthonormal extends beyond just vectors. In functional analysis, functions can also form orthonormal sets under certain inner product definitions. For instance, the sine and cosine functions over an interval can be considered orthonormal with respect to the L2 inner product. This property is particularly useful in Fourier series, where functions are decomposed into orthonormal components, facilitating the analysis of periodic functions. To summarize, the term orthonormal encapsulates a fundamental idea in mathematics that combines the notions of orthogonality and normalization. Whether in theoretical studies or practical applications, orthonormal vectors and functions provide a powerful framework for understanding complex systems and performing calculations efficiently. As we delve deeper into the realms of mathematics and science, the importance of orthonormal entities continues to grow, underscoring their value in both academic research and real-world applications.

在数学和物理学领域，正交归一向量的概念在各种应用中起着至关重要的作用，尤其是在线性代数和泛函分析中。要理解正交归一的含义，我们首先需要将其拆分成几个组成部分。“正交”一词指的是彼此垂直的向量，而“归一”则表示这些向量具有单位长度，即大小等于一。因此，如果一组向量既是正交的又是归一的，那么它们就被认为是正交归一的。 正交归一向量的重要性可以在众多数学背景中看到。例如，在欧几里得空间的领域中，任何二维向量都可以表示为两个正交归一基向量的线性组合。这种简化使得计算更容易，几何解释更清晰。当向量是正交归一时，涉及点积的计算变得简单，因为任何两个不同的正交归一向量的点积等于零，而一个向量与自身的点积等于一。 在ℝ^n的标准基中，可以找到正交归一向量的例子，其中向量e1 = (1, 0)，e2 = (0, 1)，等等，都是正交归一的。这些基向量不仅表示空间中的方向，还作为构建该空间中其他向量的基础。通过将任何向量表示为这些正交归一基向量的组合，可以简化许多操作，例如投影和变换。 除了其数学优雅性外，正交归一向量在计算机图形学、量子力学和信号处理等多个领域也有实际应用。在计算机图形学中，正交归一基用于定义坐标系统，使图像渲染更加高效。在量子力学中，量子系统的状态可以使用正交归一向量在希尔伯特空间中表示，这使物理学家能够准确计算概率和期望。 此外，正交归一的概念超越了向量本身。在泛函分析中，函数也可以在某些内积定义下形成正交归一集合。例如，正弦和余弦函数在一个区间上可以被认为是相对于L2内积的正交归一的。这一属性在傅里叶级数中尤其有用，在傅里叶级数中，函数被分解为正交归一分量，从而便于对周期函数的分析。 总之，术语正交归一概括了数学中的一个基本思想，结合了正交性和归一化的概念。无论是在理论研究还是实际应用中，正交归一向量和函数为理解复杂系统和高效执行计算提供了强大的框架。当我们深入探讨数学和科学的领域时，正交归一实体的重要性不断增长，突显了它们在学术研究和现实世界应用中的价值。