Eigenvalues of Words in Two Positive Definite Letters

Details Eigenvalues of Words in Two Positive Definite Letters Eigenvalues of Words in Two Positive Definite Letters

2005-11-16

arxiv.org/abs/math/0511411v1

Mathematics

Operator Algebras

13 pages, SIAM Journal of Matrix Analysis

Scientific paper

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.

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