The closed hyperbolicity cone of a hyperbolic polynomial 
with respect to 
is the set of 
for which every root of 
is nonnegative.
Writing these roots as 
, ..., 
gives
 |
It is a closed set and a convex cone (Netzer and Sanyal 2015). For the determinant 
on real symmetric matrices and 
, the identity matrix,
the roots are the eigenvalues
of 
,
so the cone set consists of the positive
semidefinite matrices.
