associated matrix

简明释义

结合阵;

英英释义

例句

1.In machine learning, the performance of the algorithm can often be evaluated using an associated matrix 关联矩阵 that compares predicted and actual outcomes.

在机器学习中，算法的性能通常可以通过一个关联矩阵 associated matrix 来评估，它比较了预测结果和实际结果。

2.The associated matrix 关联矩阵 in this network analysis helps to identify relationships between nodes.

在这个网络分析中，关联矩阵 associated matrix 帮助识别节点之间的关系。

3.To understand the data structure better, we created an associated matrix 关联矩阵 to visualize the connections.

为了更好地理解数据结构，我们创建了一个关联矩阵 associated matrix 来可视化连接。

4.The associated matrix 关联矩阵 generated from the survey data reveals significant trends among participants.

从调查数据生成的关联矩阵 associated matrix 显示了参与者之间的重要趋势。

5.Using an associated matrix 关联矩阵 allows researchers to determine the strength of relationships in their data.

使用关联矩阵 associated matrix 可以让研究人员确定数据中关系的强度。

作文

In the realm of mathematics and computer science, the term associated matrix refers to a specific type of matrix that is linked to a set of linear equations or a particular mathematical structure. Understanding the concept of an associated matrix is crucial for students and professionals alike, as it serves as a foundational element in various applications, including data analysis, machine learning, and optimization problems.To begin with, an associated matrix can be defined as a matrix that represents the relationships between different variables in a system. For example, in linear algebra, when dealing with a system of linear equations, the coefficients of these equations can be organized into an associated matrix. This matrix not only encapsulates the information about the equations but also provides a means to solve them using various techniques such as Gaussian elimination or matrix inversion.Moreover, the concept of an associated matrix extends beyond just linear equations. In graph theory, for instance, the adjacency matrix of a graph serves as an associated matrix that illustrates the connections between nodes. Each entry in this matrix indicates whether pairs of vertices are adjacent or not, thereby allowing for the analysis of properties such as connectivity and pathfinding within the graph.Another important application of the associated matrix is in the field of statistics and data science. When performing multivariate analysis, researchers often construct an associated matrix to represent the relationships among multiple variables. This matrix can help in understanding correlations, variances, and covariances, ultimately aiding in building predictive models that rely on these statistical relationships.Furthermore, in machine learning, especially in techniques like Principal Component Analysis (PCA), the associated matrix plays a vital role. PCA involves transforming data into a new coordinate system where the greatest variance lies along the first coordinate (the principal component). The covariance matrix, which is an associated matrix, is computed from the data to identify these directions of maximum variance, thus facilitating dimensionality reduction and feature extraction.In conclusion, the associated matrix is a versatile and powerful tool in various fields of study. Its ability to succinctly represent complex relationships among variables makes it invaluable in solving equations, analyzing graphs, conducting statistical analyses, and implementing machine learning algorithms. As we continue to explore the depths of mathematics and its applications, a solid grasp of the concept of the associated matrix will undoubtedly enhance our problem-solving skills and analytical capabilities. By recognizing the significance of this matrix, we can better appreciate its role in advancing technology and understanding the world around us.

在数学和计算机科学领域，术语关联矩阵指的是与一组线性方程或特定数学结构相关联的一种特定类型的矩阵。理解关联矩阵的概念对学生和专业人士来说至关重要，因为它在数据分析、机器学习和优化问题等各种应用中都起着基础性作用。首先，关联矩阵可以定义为一个表示系统中不同变量之间关系的矩阵。例如，在处理线性方程组时，这些方程的系数可以组织成一个关联矩阵。这个矩阵不仅包含了关于方程的信息，还提供了一种使用高斯消元法或矩阵求逆等各种技术来解决这些方程的方法。此外，关联矩阵的概念不仅限于线性方程。在图论中，例如，图的邻接矩阵作为一个关联矩阵，展示了节点之间的连接关系。这个矩阵中的每个条目指示一对顶点是否相邻，从而允许分析图的连通性和路径查找等属性。关联矩阵的另一个重要应用是在统计学和数据科学领域。当进行多元分析时，研究人员通常构建一个关联矩阵来表示多个变量之间的关系。这个矩阵可以帮助理解相关性、方差和协方差，最终有助于建立依赖于这些统计关系的预测模型。此外，在机器学习中，特别是在主成分分析（PCA）等技术中，关联矩阵发挥着至关重要的作用。PCA涉及将数据转换为一个新的坐标系，其中最大方差沿着第一个坐标（主成分）方向。协方差矩阵，即关联矩阵，是从数据中计算得出的，用于识别这些最大方差的方向，从而促进降维和特征提取。总之，关联矩阵是各个研究领域中一种多功能且强大的工具。它能够简洁地表示变量之间复杂的关系，使其在解决方程、分析图形、进行统计分析和实施机器学习算法方面不可或缺。随着我们继续探索数学及其应用的深度，牢固掌握关联矩阵的概念无疑将增强我们的解决问题能力和分析能力。通过认识到这个矩阵的重要性，我们可以更好地欣赏它在推动技术进步和理解周围世界中的作用。