Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

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Hillar, Christopher; Johnson, Charles R.;
  • Subject: Mathematics - Operator Algebras | Mathematics - Spectral Theory | 15A57, 15A90, 81Q99, 20F10, 15A42, 15A23
    arxiv: Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) | Computer Science::Formal Languages and Automata Theory

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 lon... View more
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