Tropical linear algebra with the Łukasiewicz T-norm
Copyright policy )Tropical linear algebra with the Łukasiewicz T-norm
The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Lukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-Lukasiewicz semiring.
27 pages
- University of Birmingham United Kingdom
- University of Birmingham
- UNIVERSITY OF BIRMINGHAM
- University of Hradec Králové Czech Republic
- University of Birmingham Finland
tropical linear algebra, Eigenvalues, singular values, and eigenvectors, Logic, Matrix power, Eigenvector, Max-plus, eigenvector, matrix power, Tropical, Łukasiewicz, Logical aspects of Łukasiewicz and Post algebras, max-plus linear algebra, Artificial Intelligence, FOS: Mathematics, Mathematics - Combinatorics, Łukasiewicz linear algebra, Combinatorics (math.CO), Max-plus and related algebras
tropical linear algebra, Eigenvalues, singular values, and eigenvectors, Logic, Matrix power, Eigenvector, Max-plus, eigenvector, matrix power, Tropical, Łukasiewicz, Logical aspects of Łukasiewicz and Post algebras, max-plus linear algebra, Artificial Intelligence, FOS: Mathematics, Mathematics - Combinatorics, Łukasiewicz linear algebra, Combinatorics (math.CO), Max-plus and related algebras
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