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Abstract
The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all elements of X1 AX are less than or equal to the maximum cycle geometric mean of A, with strict inequality for the entries which do not fie on critical cycles. In this paper such scalings are described by means of the max algebraic subeigenvectors and Kleene stars of nonnegative matrices as well as by some concepts of convex geometry. (c) 2009 Elsevier Inc. All rights reserved.
Original language  English 

Pages (fromto)  23952406 
Number of pages  12 
Journal  Linear Algebra and its Applications 
Volume  431 
Issue number  12 
DOIs  
Publication status  Published  1 Dec 2009 
Keywords
 Subeigenvectors
 Max algebra
 Kleene star
 Diagonal similarity
 Convex cones
 Tropical convexity
 Matrix scaling
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Dive into the research topics of 'On visualization scaling, subeigenvectors and Kleene stars in max algebra'. Together they form a unique fingerprint.Projects
 1 Finished

Feasibility and Reachability in MaxLinear Systems
Butkovic, P.
Engineering & Physical Science Research Council
1/02/08 → 30/04/11
Project: Research Councils