Description

In the paper "Stable and Real-Zero Polynomials in Two-Variables" by Grinshpan, Kaliuzhnyi-Verbovetskyi, Vinnikov, Woerdeman, they reduce constructing a Hermitian determinantal representation for trivariate hyperbolic polynomials to constructing a certain factorization of a positive definite valued matrix polynomial. I will present this derivation and then present an elementary proof of the existence of these factorizations following the paper "A Simple Proof of the Matrix-Valued Fejer-Riesz Theorem" by Ephremidze, Janashia, and Lagvilava.