subspace

简明释义

英[ˈsʌbˌspeɪs]美[ˈsʌbˌspeɪs]

n. 子空间

英英释义

单词用法

同义词

反义词

例句

1.Methods Using the invariant subspace method.

方法利用不变子空间方法。

2.Scientists on Earth first confirm existence of the subspace domain.

地球科学家首次确认子空间的存在。

3.The total least squares method was used in the improved algorithm to obtain the noise subspace.

改进算法利用总体最小二乘法得到噪声子空间。

4.In this paper. We intreoduce the concept of inferior subspace and invariant inferior subspace and also explores some natures of them.

本文给出了次子空间与不变次子空间的概念，并探讨了它们的一些性质。

5.The key issue in stochastic subspace identification is to obtain the order of the system.

在随机子空间识别方法中，确定系统的阶数是该方法的关键工作。

6.The second method is based on the virtual sub-carrier subspace blind channel estimation method.

第二种方法是基于虚拟子载波的子空间盲信道估计方法。

7.This paper presents at first the definitions of the space expanded by an array, the signal subspace and the noise subspace.

首先对基阵所张成的空间、信号子空间和噪声子空间给出了定义。

8.In the third chapter, the perturbation of invariant subspace, singular subspaces and deflating subspaces are discussed.

第三章讨论了不变子空间、奇异子空间对和收缩子空间对的扰动。

9.In computer graphics, a subspace 子空间 can refer to a lower-dimensional representation of a higher-dimensional object.

在计算机图形学中，子空间 subspace 可以指高维物体的低维表示。

10.A function space can have various subspaces 子空间 defined by different boundary conditions.

一个函数空间可以有由不同边界条件定义的各种子空间 subspaces。

11.When analyzing data, we can project our dataset onto a subspace 子空间 to reduce dimensionality.

在分析数据时，我们可以将数据集投影到一个子空间 subspace上以减少维度。

12.In linear algebra, a subspace 子空间 is a vector space that is entirely contained within another vector space.

在线性代数中，子空间 subspace 是一个完全包含在另一个向量空间中的向量空间。

13.The set of all solutions to a homogeneous linear equation forms a subspace 子空间 of the vector space.

所有齐次线性方程的解集形成一个向量空间的子空间 subspace。

作文

In mathematics, particularly in linear algebra and functional analysis, the concept of subspace (子空间) plays a crucial role in understanding vector spaces. A subspace (子空间) is essentially a smaller vector space that exists within a larger vector space. To qualify as a subspace (子空间), a set must satisfy three important criteria: it must contain the zero vector, be closed under vector addition, and be closed under scalar multiplication. These properties ensure that any linear combination of vectors in the subspace (子空间) remains within that same set, thereby preserving the structure of the vector space. For instance, consider the vector space R^3, which consists of all ordered triples of real numbers. A typical example of a subspace (子空间) within R^3 could be the xy-plane, where the z-coordinate is always zero. This plane satisfies all the conditions of a subspace (子空间): it includes the zero vector (0, 0, 0), any two vectors in the plane can be added together to produce another vector in the plane, and multiplying any vector in the plane by a scalar will also yield a vector that lies in the xy-plane. The concept of subspace (子空间) extends beyond mere mathematical definitions; it has significant applications in various fields such as physics, computer science, and engineering. For example, in quantum mechanics, the state space of a system can be thought of as a vector space, and specific states can form a subspace (子空间) representing a particular set of physical conditions. In computer graphics, transformations applied to objects can be understood through the lens of subspaces (子空间), where different transformations correspond to different subspaces (子空间) of possible states of an object. Moreover, in data science, dimensionality reduction techniques often involve projecting high-dimensional data onto a subspace (子空间) of lower dimensions. This helps in simplifying complex datasets while retaining essential information, making it easier to visualize and analyze the data. Techniques such as Principal Component Analysis (PCA) rely on identifying the subspace (子空间) that captures the most variance in the data, thus allowing for efficient data representation. In summary, the notion of a subspace (子空间) is fundamental in mathematics and has far-reaching implications across various disciplines. By understanding what constitutes a subspace (子空间) and its properties, one gains insights into the structure and behavior of vector spaces. This understanding not only enriches mathematical knowledge but also enhances our ability to apply these concepts in practical scenarios, from theoretical physics to machine learning. As we navigate through different fields, the ability to identify and work with subspaces (子空间) becomes an invaluable skill, bridging abstract mathematical theories with real-world applications.

在数学中，特别是在线性代数和泛函分析中，子空间的概念在理解向量空间方面起着至关重要的作用。子空间是存在于更大向量空间中的一个较小的向量空间。要符合子空间的条件，集合必须满足三个重要标准：它必须包含零向量，在向量加法下是封闭的，并且在标量乘法下也是封闭的。这些属性确保了子空间中的任何向量组合仍然保持在同一集合内，从而保持向量空间的结构。例如，考虑向量空间R^3，它由所有有序的实数三元组组成。在R^3中，一个典型的子空间示例可能是xy平面，其中z坐标始终为零。这个平面满足子空间的所有条件：它包括零向量(0, 0, 0)，平面中的任何两个向量可以相加以产生另一个平面内的向量，乘以平面内任何向量的标量也会产生一个位于xy平面的向量。子空间的概念超越了单纯的数学定义；它在物理学、计算机科学和工程等各个领域具有重要应用。例如，在量子力学中，系统的状态空间可以被视为一个向量空间，而特定状态可以形成一个子空间，代表一组特定的物理条件。在计算机图形学中，施加于对象的变换可以通过子空间的视角来理解，不同的变换对应于对象可能状态的不同子空间。此外，在数据科学中，降维技术通常涉及将高维数据投影到较低维度的子空间中。这有助于简化复杂的数据集，同时保留重要信息，使得数据更易于可视化和分析。主成分分析(PCA)等技术依赖于识别捕获数据中最大方差的子空间，从而实现高效的数据表示。总之，子空间的概念在数学中是基础性的，并在各个学科中具有深远的影响。通过理解什么构成子空间及其属性，人们可以深入了解向量空间的结构和行为。这种理解不仅丰富了数学知识，还增强了我们在实际场景中应用这些概念的能力，从理论物理到机器学习。当我们在不同领域中穿行时，识别和处理子空间的能力成为一项宝贵的技能，架起了抽象数学理论与现实世界应用之间的桥梁。