A hyperbolic polynomial with respect to a vector 
is a homogeneous
polynomial 
with real coefficients
and positive total degree,
such that 
and 
has only real roots for every 
(Netzer and Sanyal 2015). For example, 
is hyperbolic with respect to 
because 
. The signs of these roots
determine the associated hyperbolicity cone.
Hyperbolic Polynomial
See also
Homogeneous Polynomial, Hyperbolicity Cone, Real RootExplore with Wolfram|Alpha
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. "Hyperbolic Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HyperbolicPolynomial.html