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Mathematics > Numerical Analysis

arXiv:2205.13245 (math)
[Submitted on 26 May 2022]

Title:Projectively and weakly simultaneously diagonalizable matrices and their applications

Authors:Wentao Ding, Jianze Li, Shuzhong Zhang
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Abstract:Characterizing simultaneously diagonalizable (SD) matrices has been receiving considerable attention in the 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, T_{m,n}-SD (SDO), DWSD and D_{m,n}-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 (QCQP) and independent component analysis (ICA).
Comments: 39 pages
Subjects: Numerical Analysis (math.NA)
MSC classes: 15A20, 15A21, 15A22, 90C20, 90C30
Cite as: arXiv:2205.13245 [math.NA]
  (or arXiv:2205.13245v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2205.13245

Submission history

From: Jianze Li [view email]
[v1] Thu, 26 May 2022 09:31:42 UTC (51 KB)
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