# On the spectral properties of real anti-tridiagonal Hankel matrices

## TL;DR

This paper investigates the spectral properties of real anti-tridiagonal Hankel matrices by expressing their eigenvalues as zeros of rational functions and deriving their eigenvectors based on these eigenvalues.

## Contribution

It introduces a novel method to determine eigenvalues and eigenvectors of these structured matrices using rational functions, expanding understanding of their spectral characteristics.

## Key findings

- Eigenvalues are characterized as zeros of specific rational functions.
- Eigenvectors can be derived once eigenvalues are known.
- Provides a new analytical approach for spectral analysis of structured matrices.

## Abstract

In this paper we express the eigenvalues of real anti-tridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues.