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

Authors:
Martin Gavalec;Ján Plavka
Affiliations:
Faculty of Informatics and Management, Department of Information Technologies, University of Hradec Králové, Rokitanského 62, 50003 Hradec Králové, Czech Republic;Faculty of Electrical Engineering and Informatics, Department of Mathematics, Technical University in Košice, B. Nmcovej 32, 04200 Košice, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2007

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