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Computing the determinantal representations of hyperbolic forms

Mao-Ting ChienHiroshi Nakazato — 2016

Czechoslovak Mathematical Journal

The numerical range of an n × n matrix is determined by an n degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an n degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus g = 1 . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus g = 0 , 1 , and present an elementary computation...

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