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, Tm,n-SD (SDO), DWSD, and Dm,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 and independent component analysis.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 167-202 |
| Number of pages | 36 |
| Journal | SIAM Journal on Matrix Analysis and Applications |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2024 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024 Society for Industrial and Applied Mathematics Publications. All rights reserved.
Keywords
- canonical form
- independent component analysis
- projective simultaneous diagonalization
- quadratically constrained quadratic programming
- simultaneous diagonalization
- weak simultaneous diagonalization