Structure and dimension of the eigenspace of a concave Monge matrix

Abstract

The eigenspace structure for a given n × n concave Monge matrix in a max-plus algebra is described. Based on the description, an O ( n ) algorithm for computing the eigenspace dimension is formulated, which is faster than the previously known algorithms. Analogous results for convex Monge matrices have been published in [M. Gavalec, J. Plavka, Structure of the eigenspace of a Monge matrix in max-plus algebra, Discrete Appl. Math. 156 (2008) 596–606].