Real Factorization of Positive Semidefinite Matrix Polynomials

Sarah Gift, Hugo J. Woerdeman

Suppose $Q(x)$ is a real $n\times n$ regular symmetric positive semidefinite matrix polynomial. Then it can be factored as $$Q(x)=G(x{)}^{T}G(x),$$ where $G(x)$ is a real $n\times n$…