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Abstract
We study the maxalgebraic analogue of equations involving Zmatrices and Mmatrices, with an outlook to a more general algebraic setting. We show that these equations can be solved using the Frobenius tracedown method in a way similar to that in nonnegative linear algebra [G.F. Frobenius, Über Matrizen aus nicht negativen Elementen. Sitzungsber. Kön. Preuss. Akad. Wiss., 1912, in Ges. Abh., Vol. 3, Springer, 1968, pp. 546–557; D. Hershkowitz and H. Schneider, Solutions of Zmatrix equations, Linear Algebra Appl. 106 (1988), pp. 25–38; H. Schneider, The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: A survey, Linear Algebra Appl. 84 (1986), pp. 161–189], characterizing the solvability in terms of supports and access relations. We give a description of the solution set as combination of the least solution and the eigenspace of the matrix, and provide a general algebraic setting in which this result holds.
Original language  English 

Pages (fromto)  11911210 
Number of pages  20 
Journal  Linear and Multilinear Algebra 
Volume  60 
Issue number  10 
DOIs  
Publication status  Published  6 Feb 2012 
Keywords
 maxalgebra
 nonnegative linear algebra
 idempotent semiring
 Zmatrix equations
 Kleene star
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Dive into the research topics of 'Zmatrix equations in maxalgebra, nonnegative linear algebra and other semirings'. Together they form a unique fingerprint.Projects
 1 Finished

PerronFrobenius Theory and MaxAlgebraic Combinatorics of Nonnegative Matrices
Butkovic, P.
Engineering & Physical Science Research Council
12/03/12 → 11/03/14
Project: Research Councils