Norms on complex matrices induced by complete homogeneous symmetric polynomials
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Dokumenter
- Fulltext
Forlagets udgivne version, 233 KB, PDF-dokument
We introduce a remarkable new family of norms on the space of (Formula presented.) complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in non-commuting variables. Our norms enjoy many desirable analytic and algebraic properties, such as an elegant determinantal interpretation and the ability to distinguish certain graphs that other matrix norms cannot. Furthermore, they give rise to new dimension-independent tracial inequalities. Their potential merits further investigation.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Bulletin of the London Mathematical Society |
Vol/bind | 54 |
Udgave nummer | 6 |
Sider (fra-til) | 2078-2100 |
ISSN | 0024-6093 |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
Stephan Ramon Garcia supported by NSF grants DMS‐1800123 and DMS‐2054002. Jurij Volčič supported by NSF grant DMS‐1954709, and by Villum Fonden via the Villum Young Investigator grant (No. 37532).
Publisher Copyright:
© 2022 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.
ID: 317817409