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

Abstract

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 π , such that the closure of S A is a subset of the set of all eigenvectors permuted by π . The simple image set of the matrix square and the topological aspects of the problem are also described.