A Canonical Form for Max Plus Symmetric Matrices and Applications

TL;DR

This paper introduces a canonical form for max plus symmetric matrices, enabling new insights into eigenvector problems and matrix commutation within the max plus algebra framework.

Contribution

It develops a canonical form for max plus symmetric matrices and applies it to eigenvector problems and matrix commutation analysis.

Findings

Canonical form for max plus symmetric matrices

Characterization of matrices commuting with a given symmetric matrix

Applications to generalized eigenvector problems

Abstract

We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that commute with a given symmetric matrix.