Simple image set of linear mappings in a max-min algebra |
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Authors: | Martin Gavalec |
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Affiliation: | a Faculty of Informatics and Management, Department of Information Technologies, University of Hradec Králové, Rokitanského 62, 50003 Hradec Králové, Czech Republic b Faculty of Electrical Engineering and Informatics, Department of Mathematics, Technical University in Košice, B. Němcovej 32, 04200 Košice, Slovakia |
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Abstract: | For a given linear mapping, determined by a square matrix A in a max-min algebra, the set SA 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 SA 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 SA 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. |
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Keywords: | primary, 15A06 secondary, 15A33 |
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