Eigenvalues of Words in Two Positive Definite Letters

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

The question of whether all words in two real positive definite letters have only positive eigenvalues is addressed and settled (negatively). This question was raised some time ago in connection with a long-standing problem in theoretical physics. A large class of words that do guarantee positive eigenvalues is identified, and considerable evidence is given for the conjecture that no other words do. In the process, a fundamental question about solvability of symmetric word equations is encountered.
13 pages, SIAM Journal of Matrix Analysis

Keywords

Operator Algebras, Rings and Algebras, 15A24, 15A57; 15A18, 15A90

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/104951

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511411
 http://arxiv.org/abs/math/0511411

Collections

arXiv