Simple image set of linear mappings in a max-min algebra

For a given linear mapping, determined by a square matrix A in a max-min algebra, the set S-A consisting of all vectors with a unique pre-image (in short: the simple image set of A) is considered. It is shown that if the matrix A is generally trapezoidal, then the closure of S-A is a subset of the set of all eigenvectors of A. In the general case, there is a permutation pi, such that the closure of S-A is a subset of the set of all eigenvectors; permuted by pi. The simple image set of the matrix square and the topological aspects of the problem are also described. (c) 2006 Elsevier B.V. All rights reserved.