The geometric generalized Lax conjecture asserts that every closed hyperbolicity cone is a spectrahedron (Netzer and Sanyal
2015). For a cone set 
, this means that there are real symmetric matrices 
, ..., 
of some common finite size with
The assertion does not require the defining hyperbolic
polynomial itself to be a determinant.
See also
Hyperbolic Polynomial,
Hyperbolicity Cone,
Projected
Lax Conjecture,
Spectrahedron
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References
Netzer, T. and Sanyal, R. "Smooth Hyperbolicity Cones Are Spectrahedral Shadows." Math. Program. 153, 213-221, 2015.
https://doi.org/10.1007/s10107-014-0744-6.
Cite this as:
Weisstein, Eric W. "Generalized Lax Conjecture."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralizedLaxConjecture.html
Subject classifications
