Eigenvalues of Words in Two Positive Definite Letters
Operator Algebras
2007-05-23 v1 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.math/0511411,
title = {Eigenvalues of Words in Two Positive Definite Letters},
author = {Christopher J Hillar and Charles R Johnson},
journal= {arXiv preprint arXiv:math/0511411},
year = {2007}
}
Comments
13 pages, SIAM Journal of Matrix Analysis