submatrix

简明释义

英[ˈsʌbˌmeɪtrɪks]美[sʌbˈmeɪtrɪks]

n. 子阵

复 数 s u b m a t r i c e s 或 s u b m a t r i x e s

英英释义

单词用法

同义词

反义词

例句

1.The generalized inverse of partitioned matrices and the expression of generalized inverse using maximal nonsingular submatrix are discussed.

摘要讨论了分块矩阵的广义逆，以及用矩阵的满秩子块表示广义逆。

2.This paper considers the problem of constructing a special kind of matrices from defective eigenpairs and the leading principal submatrix.

本文主要讨论了由给定的主子阵和两个缺损特征对构造一类特殊矩阵的问题。

3.The principal submatrix of the asymmetrical generalized positive definite matrix is not asymmetrical generalized positive definite matrix in general.

指出非对称广义正定矩阵的主子矩阵一般不是非对称广义正定矩阵。

4.The matrix extension problem is, under some constrained conditions, constructing a matrix A with a given matrix A_0 as its submatrix.

矩阵扩充问题是在某种约束条件下构造矩阵A，使得矩阵A的一个子矩阵为A_0。

5.In this paper, feasibility concerning the pole placement of generalized system was discussed by a theorem and the existence of submatrix Awas solved.

本文通过一个定理，给出了广义系统极点配置的可行性，解决了分块阵的子块的存在性问题。

6.The principal submatrix of the asymmetrical generalized positive definite matrix is not asymmetrical generalized positive definite matrix in general.

指出非对称广义正定矩阵的主子矩阵一般不是非对称广义正定矩阵。

7.The submatrix method makes the definition of mistuning parameters more freely and adds the model modification function to this identification method.

采用子矩阵型技术使得失谐参数定义更加的自由，并使得该方法具有模型修正的功能；

8.The algorithm computes the determinant of a submatrix 子矩阵 to optimize performance.

该算法计算一个submatrix 子矩阵的行列式以优化性能。

9.A submatrix 子矩阵 can be used to represent a smaller section of an image in computer vision tasks.

在计算机视觉任务中，submatrix 子矩阵 可用于表示图像的较小部分。

10.In linear algebra, a submatrix 子矩阵 can be obtained by deleting certain rows and columns from a larger matrix.

在线性代数中，通过删除较大矩阵的某些行和列，可以得到一个submatrix 子矩阵。

11.To solve the problem, we need to extract a specific submatrix 子矩阵 from the given data set.

为了解决这个问题，我们需要从给定的数据集中提取一个特定的submatrix 子矩阵。

12.Finding the largest contiguous submatrix 子矩阵 of 1s in a binary matrix is a common coding interview question.

在二进制矩阵中寻找最大的连续submatrix 子矩阵 1是一个常见的编码面试问题。

作文

In the field of mathematics and computer science, the concept of a submatrix (子矩阵) is crucial for various applications, particularly in linear algebra and data analysis. A submatrix refers to a smaller matrix that is derived from a larger matrix by selecting specific rows and columns. Understanding how to identify and manipulate submatrices can enhance one's ability to solve complex problems efficiently.Consider a scenario where we have a large matrix representing data, such as an image or a dataset with multiple attributes. Each element in this matrix can hold significant information, and sometimes we need to focus on a specific part of this data. This is where the concept of a submatrix becomes useful. For instance, if we have a 5x5 matrix but are only interested in a 2x2 section of it, we can extract that section to form a submatrix.The process of extracting a submatrix involves selecting the desired rows and columns from the original matrix. This operation is not only straightforward but also essential for various algorithms, including those used in image processing, machine learning, and statistical analysis. By working with submatrices, we can simplify computations and focus on the relevant parts of the data without being overwhelmed by the entire dataset.Moreover, submatrices play a vital role in matrix operations such as addition, multiplication, and finding determinants. For example, when multiplying two matrices, if we only need to consider a certain area of interest, we can limit our calculations to the corresponding submatrices. This targeted approach reduces computational complexity and increases efficiency.In practical applications, submatrices are often used in algorithms that require dynamic programming techniques. For instance, in solving optimization problems, we frequently deal with large matrices where only specific submatrices contribute to the optimal solution. Identifying these submatrices allows us to break down a problem into smaller, more manageable parts, making it easier to analyze and solve.Another interesting application of submatrices is in data mining and machine learning, where they can represent features or subsets of data. When training a model, it is common to work with submatrices that contain only the most relevant features, thereby enhancing the model's performance and reducing overfitting. By focusing on submatrices that capture the essence of the data, we can achieve better results with fewer resources.In conclusion, the concept of a submatrix (子矩阵) is an essential component in various mathematical and computational fields. Mastering the identification and manipulation of submatrices enables individuals to tackle complex problems more effectively. Whether in linear algebra, data analysis, or algorithm development, the ability to work with submatrices opens up new avenues for exploration and innovation. As technology continues to advance, the relevance of submatrices will only grow, making it a fundamental concept for students and professionals alike.

在数学和计算机科学领域，子矩阵的概念对于各种应用至关重要，特别是在线性代数和数据分析中。子矩阵是指通过选择特定行和列从较大矩阵派生出的较小矩阵。理解如何识别和操作子矩阵可以增强一个人有效解决复杂问题的能力。考虑一个场景，我们有一个大型矩阵表示数据，例如图像或具有多个属性的数据集。这个矩阵中的每个元素都可以保存重要信息，有时我们需要专注于这些数据的特定部分。这就是子矩阵概念变得有用的地方。例如，如果我们有一个5x5的矩阵，但只对其中的2x2部分感兴趣，我们可以提取该部分形成一个子矩阵。提取子矩阵的过程涉及从原始矩阵中选择所需的行和列。这个操作不仅简单，而且对于各种算法至关重要，包括图像处理、机器学习和统计分析等。通过使用子矩阵，我们可以简化计算，专注于数据的相关部分，而不被整个数据集所淹没。此外，子矩阵在矩阵运算中也起着重要作用，例如加法、乘法和求行列式。例如，在乘以两个矩阵时，如果我们只需要考虑某个感兴趣的区域，我们可以将计算限制在相应的子矩阵上。这种针对性的方法减少了计算复杂性，提高了效率。在实际应用中，子矩阵常常用于需要动态规划技术的算法中。例如，在解决优化问题时，我们经常处理大型矩阵，其中只有特定的子矩阵对最佳解有所贡献。识别这些子矩阵使我们能够将问题分解为更小、更易于管理的部分，从而更容易进行分析和解决。另一个有趣的子矩阵应用是在数据挖掘和机器学习中，它们可以表示特征或数据的子集。在训练模型时，通常会使用包含最相关特征的子矩阵，从而提高模型的性能并减少过拟合。通过专注于捕捉数据本质的子矩阵，我们可以在更少的资源下获得更好的结果。总之，子矩阵是各种数学和计算领域的重要组成部分。掌握子矩阵的识别和操作使个人能够更有效地解决复杂问题。无论是在线性代数、数据分析还是算法开发中，能够使用子矩阵为探索和创新开辟了新途径。随着技术的不断进步，子矩阵的相关性只会增加，使其成为学生和专业人士必须掌握的基本概念。