orthogonalizing

简明释义

英[ˌɔrˈθɑɡənəlaɪzɪŋ]美[ˌɔrˈθɑɡənəlaɪzɪŋ]

vt. 使成为正交；使正交化

第 三 人 称 单 数 o r t h o g o n a l i z e s

现 在 分 词 o r t h o g o n a l i z i n g

过 去 式 o r t h o g o n a l i z e d

过 去 分 词 o r t h o g o n a l i z e d

英英释义

单词用法

同义词

反义词

例句

1.This paper presents a new method named "Analytic Orthogonalization", for orthogonalizing direction cosine matrix.

本文提出方向余弦矩阵正交化的一种新方法——解析正交化。

2.This paper presents a new method named "Analytic Orthogonalization", for orthogonalizing direction cosine matrix.

本文提出方向余弦矩阵正交化的一种新方法——解析正交化。

3.The process of orthogonalizing the vectors ensures they are independent from each other.

对这些向量进行正交化的过程确保它们彼此独立。

4.In machine learning, orthogonalizing features can improve model performance by reducing multicollinearity.

在机器学习中，正交化特征可以通过减少多重共线性来提高模型性能。

5.The team focused on orthogonalizing their research methods to avoid overlapping results.

团队专注于正交化他们的研究方法，以避免结果重叠。

6.By orthogonalizing the design elements, we were able to create a more cohesive product.

通过正交化设计元素，我们能够创造出更具凝聚力的产品。

7.The software uses algorithms for orthogonalizing data inputs to enhance processing speed.

该软件使用算法对数据输入进行正交化以提高处理速度。

作文

In the field of mathematics and engineering, the concept of orthogonality plays a crucial role in various applications. One of the processes that involve this concept is orthogonalizing, which refers to the method of transforming a set of vectors into a new set that are mutually perpendicular or orthogonal to each other. This transformation is significant because it simplifies many mathematical operations and enhances the efficiency of algorithms used in computational tasks. To understand the importance of orthogonalizing vectors, we can consider the example of signal processing. In this context, signals can be represented as vectors in a multi-dimensional space. When these signals are orthogonalized, it allows for better separation of different signals, reducing interference and improving clarity. This is particularly beneficial in applications such as audio and image compression, where maintaining the integrity of the original signal is paramount. Moreover, orthogonalizing is not limited to just vectors; it also applies to functions in functional analysis. For instance, in the context of Fourier series, the sine and cosine functions are orthogonalized over a specific interval. This property allows for the decomposition of complex periodic functions into simpler components, facilitating easier analysis and synthesis of signals. In addition to its applications in engineering and mathematics, the concept of orthogonalizing can also be found in statistics, particularly in the method of least squares. When fitting a model to data, it is often necessary to orthogonalize the predictor variables to eliminate multicollinearity. By doing so, we ensure that the estimates of the model parameters are more stable and reliable, leading to better predictions. Furthermore, in machine learning, orthogonalizing features can improve the performance of algorithms. When training models, having features that are orthogonalized helps in reducing redundancy and enhances the learning process. This is particularly evident in techniques like Principal Component Analysis (PCA), where high-dimensional data is transformed into a lower-dimensional space while preserving variance, effectively orthogonalizing the principal components. In conclusion, the process of orthogonalizing is a fundamental technique that finds applications across various fields, including mathematics, engineering, statistics, and machine learning. By transforming vectors or functions into an orthogonal set, we can simplify complex problems, enhance computational efficiency, and achieve better results in analysis and prediction. Understanding and applying the concept of orthogonalizing is essential for anyone looking to delve deeper into these disciplines and utilize their principles effectively in real-world scenarios.

在数学和工程领域，正交性这一概念在各种应用中扮演着至关重要的角色。涉及这个概念的过程之一是orthogonalizing，它指的是将一组向量转换为一组相互垂直或正交的新向量的方法。这种转换非常重要，因为它简化了许多数学运算，并提高了计算任务中使用的算法的效率。 为了理解orthogonalizing向量的重要性，我们可以考虑信号处理的例子。在这个背景下，信号可以表示为多维空间中的向量。当这些信号被orthogonalized时，可以更好地分离不同的信号，减少干扰，提高清晰度。这在音频和图像压缩等应用中尤其有利，其中保持原始信号的完整性至关重要。 此外，orthogonalizing不仅限于向量；它还适用于函数分析中的函数。例如，在傅里叶级数的背景下，正弦和余弦函数在特定区间内是orthogonalized的。这一特性允许将复杂的周期函数分解为更简单的组件，从而便于信号的分析和合成。 除了在工程和数学中的应用外，orthogonalizing的概念在统计学中也可以找到，特别是在最小二乘法中。当将模型拟合到数据时，通常需要orthogonalize预测变量以消除多重共线性。通过这样做，我们确保模型参数的估计更加稳定和可靠，从而导致更好的预测。 此外，在机器学习中，orthogonalizing特征可以提高算法的性能。在训练模型时，具有orthogonalized特征有助于减少冗余并增强学习过程。这在主成分分析（PCA）等技术中尤为明显，其中高维数据被转换为低维空间，同时保留方差，有效地orthogonalizing主成分。 总之，orthogonalizing过程是一种基本技术，广泛应用于数学、工程、统计学和机器学习等多个领域。通过将向量或函数转化为正交集，我们可以简化复杂问题，提高计算效率，并在分析和预测中获得更好的结果。理解和应用orthogonalizing的概念对于任何希望深入这些学科并有效利用其原理于现实场景的人来说都是至关重要的。