Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

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dc.creatorHillar, Christopher
dc.creatorJohnson, Charles R.
dc.date2005-04-29
dc.date.accessioned2026-07-07T05:19:30Z
dc.date.available2026-07-07T05:19:30Z
dc.descriptionWe 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.
dc.description13 Pages, Novel Approaches to Hard Discrete Optimization, Fields Institute Communications
dc.identifierhttps://arxiv.org/abs/math/0504587
dc.identifierhttp://arxiv.org/abs/math/0504587
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75039
dc.subjectOperator Algebras
dc.subjectSpectral Theory
dc.subject15A57, 15A90, 81Q99, 20F10, 15A42, 15A23
dc.titlePositive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices
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