Monotone eigenspace structure in max-min algebra

AbstractFor 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 2n−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(n2) 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)