Characteristic Polynomials of Supertropical 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.

Key Words:

• Characteristic polynomial
• Powers of matrices
• Tropical and supertropical linear algebra

2010 Mathematics Subject Classification:

• Primary 15A15
• Secondary 15A18, 15A80, 06F05

ACKNOWLEDGMENTS

This article is part of the author's Ph.D. thesis, which was written at Bar-Ilan University under the supervision of Prof. L. H. Rowen.

Notes

Communicated by M. Cohen.