Explicit diagonalization of an anti-triangular Cesar\'o matrix

TL;DR

This paper derives explicit formulas for the eigenvalues and eigenvectors of a special anti-triangular Cesàro matrix associated with a Markov chain, providing new insights into its spectral properties.

Contribution

It presents the first explicit diagonalization of this particular anti-triangular Cesàro matrix, advancing understanding of its spectral structure.

Findings

Closed-form expressions for all eigenvalues.

Explicit eigenvectors derived for the matrix.

Enhanced understanding of the matrix's spectral properties.

Abstract

We study a specific "anti-triangular" Cesar\'o matrix corresponding to a Markov chain. We derive closed forms for all the eigenvalues and eigenvectors of this matrix.