Pattern Properties and Spectral Inequalities in Max Algebra

Abstract

The max algebra consists of the set of real numbers, along with negative infinity, equipped with two binary operations, maximization and addition. This algebra is useful in describing certain conventionally nonlinear systems in a linear fashion. Properties of eigenvalues and eigenvectors over the max algebra that depend solely on the pattern of finite and infinite entries in the matrix are studied. Inequalities for the maximal eigenvalue of a matrix over the max algebra, motivated by those for the Perron root of a nonnegative matrix, are proved.