Monotone eigenspace structure in max-min algebra

Abstract

For a given n× n matrix A in a max-min algebra, the set of all increasing eigenvectors, in notation F ⩽(A) is studied. It is shown that F ⩽(A) is a union of at most 2 n−1 intervals, and an explicit formula for the intervals is given. Moreover, it is shown that the endpoints of these intervals can be computed in O( n 2) time or in O( n) time, if an auxiliary n× n matrix C( A) has been previously computed. The results enable a complete description of the structure of the whole eigenspace F(A) .