On the powers of matrices in bottleneck/fuzzy algebra
type: Item
instance of: scholarly article
title: On the powers of matrices in bottleneck/fuzzy algebra
zbMATH Open document ID: 0866.15009
DOI: 10.1016/0024-3795(94)00338-6
published in: Linear Algebra and its Applications
publication date: 1997-07-24T00:00:00Z
review text: The author examines max-min powers of square matrices over the semiring (\([0,1]\),max,min) [cf. \textit{M. G. Thomason}, J. Math. Analysis Appl. 57, 476-480 (1977; Zbl 0345.15007)]. She characterizes stable matrices (with convergent power sequence) by properties of the associated graph and by properties of iterative sequences of the induced quasilinear transformation \(y=Ax\). As special cases, upper-triangular and circulant matrices are considered. Results of the paper are generalized by \textit{M. Gavalec} [Periodicity of matrices and orbits in fuzzy algebra, Tatra Mt. Math. Publ. 6, 35-46 (1995; Zbl 0860.15012)].
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 951793
zbMATH Keywords: bottleneck/fuzzy algebra
zbMATH Keywords: max-min matrix product
zbMATH Keywords: max-min matrix power
zbMATH Keywords: stable matrix
zbMATH Keywords: circulant matrix
zbMATH Keywords: associated graph
author: Katarina Cechlárová
reviewed by: Józef Drewniak
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00338-6
OpenAlex ID: W2085463223
cites work: Modularity of cycles and paths in graphs
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cites work: Minimizing Wallpaper Waste, Part 1: A Class of Traveling Salesman Problems
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description: scientific article; zbMATH DE number 951793