Hyperbolic Polynomials, Hyperbolicity Cones & the General Lax Conjecture
In this lecture…
Hyperbolic Polynomials
Interlacers
Hyperbolicity Cones
Theorem [Kummer, Plaumann, Vinzant 2013] The hyperbolicity cone $\Lambda_+(h, e)$ has the following description: $$ \Lambda_+(h, e) := \{ a \in \mathbb{R}^n \mid D_a h \text{ interlaces } h \} $$