Characteristic polynomials of supertropical matrices

TL;DR

This paper explores the properties of eigenvalues and characteristic polynomials of supertropical matrices, extending classical matrix theory to the supertropical setting and analyzing how these properties behave under matrix powers.

Contribution

It introduces the behavior of eigenvalues and characteristic polynomials of supertropical matrices and their powers, providing analogs to classical matrix properties.

Findings

Eigenvalues of supertropical matrices behave similarly to classical matrices under powers.

Characteristic polynomials of supertropical matrices are characterized and related to matrix powers.

The paper establishes that powers of eigenvalues correspond to eigenvalues of powered matrices.

Abstract

Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers, and obtain the analog to the basic property of matrices that any power of an eigenvalue of a matrix is an eigenvalue of the corresponding power of the matrix.