Perturbation of Perron roots and The max-plus spectral theorem

TL;DR

This paper extends Perron theory to positive matrices over the real Puiseux field, introducing a recursive combinatorial method based on tropical linear algebra to compute Perron roots and vectors.

Contribution

It presents a novel recursive approach for calculating Perron roots and vectors of positive Puiseux matrices using tropical linear algebra techniques.

Findings

Developed a recursive method for Perron root computation

Applied tropical linear algebra to Puiseux matrices

Enhanced understanding of Perron theorem over Puiseux fields

Abstract

In this paper, we consider the Perron theorem over the real Puiseux field. We introduce a recursive method for calculating Perron roots and Perron vectors of positive Puiseux matrices (which satisfy some condition of genericness) by means of combinatorics based on the tropical linear algebra.