Remark on the eigenvalues of a tridiagonal matrix in biogeography

TL;DR

This paper discusses the eigenvalues of a specific tridiagonal matrix relevant to biogeography, building on prior work that involved the Sylvester determinant, to deepen understanding of its spectral properties.

Contribution

It provides a remark on the eigenvalues of a tridiagonal matrix in biogeography, offering insights or clarifications on the previous results by Igelnik and Simon.

Findings

Clarification of eigenvalue properties

Connection to Sylvester determinant

Implications for biogeography models

Abstract

The main result proved in [The eigenvalues of a tridiagonal matrix in biogeography, Appl. Math. Comput. 218 (2011) 195-201; MR2821464] by B. Igelnik and D. Simon is virtually the Sylvester determinant.