Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem
- Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, have been extended to the case of symplectic eigenvalues. In this note, we will generalize Williamson's diagonal form for symmetric positive-definite matrices to the case of symmetric positive-semidefinite matrices, which allows us to define symplectic eigenvalues, and prove the trace minimization theorem in the new setting.
| Author: | Nguyen Thanh SonORCiD, Tatjana StykelORCiDGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/99836 |
| URL: | https://journals.uwyo.edu/index.php/ela/article/view/7351 |
| ISSN: | 1537-9582OPAC |
| Parent Title (English): | Electronic Journal of Linear Algebra |
| Publisher: | International Linear Algebra Society |
| Place of publication: | Pensacola, FL |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2022 |
| Release Date: | 2022/11/30 |
| Volume: | 38 |
| First Page: | 607 |
| Last Page: | 616 |
| DOI: | https://doi.org/10.1254/spei/57874 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
