Computing the determinantal representations of hyperbolic forms
The numerical range of an matrix is determined by an degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an 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 . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus , and present an elementary computation...