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Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

Christopher Hillar·Charles R. Johnson
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Abstract

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. 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.

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BibTeXRIS

Christopher Hillar, Charles R. Johnson. 2005-04-29. Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices. https://arxiv.org/abs/math/0504587

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