2005/04/29 by Christopher J. Hillar, Christopher Hillar, Hillar, Christopher +2
Computer Science · Mathematics · #15A23 #15A42 #15A57 #15A90 #20F10 #81Q99 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Spectral Theory (math.SP) #math.OA #math.SP #msc:15A23 #msc:15A42 #msc:15A57 #msc:15A90 #msc:20F10 #msc:81Q99
paper · pdf · doi:10.48550/arxiv.math/0504587
13 Pages, Novel Approaches to Hard Discrete Optimization, Fields Institute Communications
arxiv created 2005/04/29 · openalex publication_date 2005/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.