Hyperbolic Polynomials, Hyperbolicity Cones & the General Lax Conjecture

In this lecture…

Hyperbolic Polynomials

Interlacers

Hyperbolicity Cones

Theorem [Kummer, Plaumann, Vinzant 2013] The hyperbolicity cone ${\mathrm{\Lambda }}_{+}(h,e)$ has the following description: $${\mathrm{\Lambda }}_{+}(h,e):=\{a\in {\mathbb{R}}^n\mid D_{a}h\text{ interlaces }h\}$$

Properties

General Lax Conjecture