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Abstract
Let a circle plus b = max(a, b) and a circle times b = a + b for a, b is an element of (R) over bar := R boolean OR {infinity}. By maxalgebra we understand the analogue of linear algebra developed for the pair of operations (circle plus, circle times), extended to matrices and vectors. The symbol A(k) stands for the kth maxalgebraic power of a square matrix A. Let us denote by epsilon the maxalgebraic "zero" vector, all the components of which are infinity. The maxalgebraic eigenvalueeigenvector problem is the following: Given A is an element of (R) over bar (n x n), find all lambda is an element of (R) over bar and x is an element of (R) over bar (n), x not equal epsilon, such that A circle times x = lambda circle times x. Certain problems of scheduling lead to the following question: Given A is an element of (R) over bar (n x n), is there a k such that A(k) circle times x is a maxalgebraic eigenvector of A? If the answer is affirmative for every x not equal epsilon, then A is called robust. First, we give a complete account of the reducible maxalgebraic spectral theory, and then we apply it to characterize robust matrices.
Original language  English 

Pages (fromto)  14121431 
Number of pages  20 
Journal  S I A M Journal on Matrix Analysis and Applications 
Volume  31 
Issue number  3 
DOIs  
Publication status  Published  1 Jan 2010 
Keywords
 maxalgebra
 eigenspace
 reducible matrix
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Dive into the research topics of 'Reducible Spectral Theory with Applications to the Robustness of Matrices in MaxAlgebra'. 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