Spectral properties of anti-heptadiagonal persymmetric Hankel matrices

TL;DR

This paper derives explicit formulas for the eigenvalues, eigenvectors, powers, and inverses of anti-heptadiagonal persymmetric Hankel matrices, facilitating their analysis and computation.

Contribution

It introduces explicit polynomial-based expressions for eigenvalues and eigenvectors, and formulas for powers and inverses of these specialized matrices, advancing their theoretical understanding.

Findings

Eigenvalues as zeros of explicit polynomials

Explicit eigenvector representations

Formulas for powers and inverses

Abstract

In this paper we express the eigenvalues of anti-heptadiagonal persymmetric Hankel matrices as the zeros of explicit polynomials giving also a representation of its eigenvectors. We present also an expression depending on localizable parameters to compute its integer powers. In particular, an explicit formula not depending on any unknown parameter for the inverse of anti-heptadiagonal persymmetric Hankel matrices is provided.