Hyperbolic systems with scaled Jordan frames have minimal defining polynomials and admit a Euclidean Jordan algebra structure via the frame.
Combinatorics hidden in hyperbolic polynomials and related topics
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abstract
The main topic of this paper is various "hyperbolic" generalizations of the Edmonds-Rado theorem on the rank of intersection of two matroids. We prove several results in this direction and pose a few questions. We also give generalizations of the Obreschkoff theorem and recent results of J. Borcea and B. Shapiro.
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math.OC 1years
2026 1verdicts
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Minimal polynomials, scaled Jordan frames, and Schur-type majorization in hyperbolic systems
Hyperbolic systems with scaled Jordan frames have minimal defining polynomials and admit a Euclidean Jordan algebra structure via the frame.