Projectively and Weakly Simultaneously Diagonalizable Matrices and their Applications

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-01-16 DOI:10.1137/22m1507656

Wentao Ding, Jianze Li, Shuzhong Zhang

引用次数: 0

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 167-202, March 2024.
Abstract. Characterizing simultaneously diagonalizable (SD) matrices has been receiving considerable attention in recent decades due to its wide applications and its role in matrix analysis. However, the notion of SD matrices is arguably still restrictive for wider applications. In this paper, we consider two error measures related to the simultaneous diagonalization of matrices and propose several new variants of SD thereof; in particular, TWSD, TWSD-B, [math]-SD (SDO), DWSD, and [math]-SD (SDO). Those are all weaker forms of SD. We derive various sufficient and/or necessary conditions of them under different assumptions and show the relationships between these new notions. Finally, we discuss the applications of these new notions in, e.g., quadratically constrained quadratic programming and independent component analysis.

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投影和弱同时可对角矩阵及其应用

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 167-202 页，2024 年 3 月。摘要。由于同时可对角化（SD）矩阵的广泛应用及其在矩阵分析中的作用，近几十年来，SD 矩阵的特征描述一直受到广泛关注。然而，可以说 SD 矩阵的概念对于更广泛的应用仍有限制。在本文中，我们考虑了与矩阵同时对角相关的两种误差度量，并提出了 SD 的几种新变体，特别是 TWSD、TWSD-B、[math]-SD (SDO)、DWSD 和 [math]-SD (SDO)。这些都是较弱形式的 SD。我们在不同的假设条件下推导出了它们的各种充分条件和/或必要条件，并展示了这些新概念之间的关系。最后，我们讨论了这些新概念在二次约束二次编程和独立分量分析等方面的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.