An explicit homogeneous hyperbolic polynomial of degree 20 in 23 real variables has a closed hyperbolicity cone that cannot be represented as the positive-semidefinite region of any finite real symmetric linear matrix pencil in the original variables.
An explicit homogeneous hyperbolic polynomial of degree 20 in 23 real variables has a closed hyperbolicity cone that cannot be represented as the positive-semidefinite region of any finite real symmetric linear matrix pencil in the original variables.
An explicit homogeneous hyperbolic polynomial of degree 20 in 23 real variables has a closed hyperbolicity cone that cannot be represented as the positive-semidefinite region of any finite real symmetric linear matrix pencil in the original variables.
If correct, disproves the geometric Generalized Lax conjecture that every hyperbolicity cone is spectrahedral.
Is every hyperbolicity cone representable by a finite symmetric positive-semidefinite pencil?
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