# Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle

## TL;DR

This paper extends known results on the interlacing of zeros of paraorthogonal polynomials on the unit circle, providing a unified approach that relates to matrices similar to unitary upper Hessenberg matrices with positive subdiagonals.

## Contribution

It offers a simple, unified extension of interlacing properties for zeros of paraorthogonal polynomials on the unit circle.

## Key findings

- Extended interlacing results for zeros of paraorthogonal polynomials.
- Unified approach applicable to matrices similar to unitary upper Hessenberg matrices.
- Clarified the relationship between polynomial zeros and matrix characteristics.

## Abstract

The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix similar to an unitary upper Hessenberg matrix with positive subdiagonal elements.