Smooth Hyperbolicity Cones are Spectrahedral Shadows

Tim Netzer; Raman Sanyal

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arXiv · 1208.0441

Smooth Hyperbolicity Cones are Spectrahedral Shadows

Tim Netzer·Raman Sanyal

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Abstract

Hyperbolicity cones are convex algebraic cones arising from hyperbolic polynomials. A well-understood subclass of hyperbolicity cones is that of spectrahedral cones and it is conjectured that every hyperbolicity cone is spectrahedral. In this paper we prove a weaker version of this conjecture by showing that every smooth hyperbolicity cone is the linear projection of a spectrahedral cone, that is, a spectrahedral shadow.

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Tim Netzer, Raman Sanyal. 2012-08-02. Smooth Hyperbolicity Cones are Spectrahedral Shadows. https://arxiv.org/abs/1208.0441

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