On the positive eigenvalues and eigenvectors of a non-negative matrix

TL;DR

This paper develops a comprehensive theory for positive eigenvalues and eigenvectors of countable, cofinal non-negative matrices, expanding understanding in spectral theory and matrix analysis.

Contribution

It introduces a general framework for analyzing positive eigenvalues and eigenvectors in countable, cofinal non-negative matrices, extending classical results.

Findings

Established conditions for existence of positive eigenvalues

Characterized positive eigenvectors in the countable, cofinal setting

Extended spectral theory to a broader class of matrices

Abstract

The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.