Characteristic polynomial of matrices over interval max-plus algebra

Abstract

Let R be the set of all real number and ? =-8. Max-plus algebra is the set R ? = R ? {?} that is equipped with maximum (?) and addition (?) operations. For each A?R ?n×n can be found its eigenvalue and its eigenvector. The problem how to find eigenvalue and eigenvector is eigenproblem. A number of methods have been developed to determine the eigenvalues of a matrix over max-plus algebra. One of them is by using characteristic polynomial. Max-plus algebra has been expanded into interval max-plus algebra. Interval max-plus algebra is the set I(R )?={x=[x_, x¯]| x_, x¯?R ,?