An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem

TL;DR

This paper presents a straightforward and concise proof of the polynomial matrix spectral factorization theorem, applicable on both the unit circle and the real line, using basic complex analysis and linear algebra techniques.

Contribution

It offers a new elementary proof of the spectral factorization theorem, simplifying previous approaches and making the proof more accessible.

Findings

Provides a simple, short proof of the spectral factorization theorem.

Applicable to polynomial matrices on the unit circle and real line.

Utilizes elementary complex analysis and linear algebra methods.

Abstract

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.