子空间之间的夹角及其正切
Angles between subspaces and their tangents
AI总结：
本文通过奇异值分解构造矩阵，使其奇异值等于子空间间主夹角的正切，并应用于特征值问题的子空间迭代收敛分析。
摘要：
子空间之间的主夹角（PABS，也称为规范角）是数学、统计学及应用（如数据挖掘）中的经典工具。传统上，PABS通过其余弦引入。PABS的余弦和正弦通常使用奇异值分解来定义。我们采用相同的思想处理正切，即通过几种方法显式构造矩阵，使其奇异值等于PABS的正切：使用子空间的正交基和非正交基，以及投影算子。这种构造有应用，例如在特征值问题的子空间迭代收敛分析中。
英文摘要：
Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomposition. We utilize the same idea for the tangents, i.e., explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and non-orthonormal bases for subspaces, as well as projectors. Such a construction has applications, e.g., in analysis of convergence of subspace iterations for eigenvalue problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
