On a proof of the general version of the spectral theorem in max-plus algebra

The so-called spectral theorem for square irreducibe matrices is well-known in the max-plus community. The theorem is a fundamental result concerning matrix powers and eigenvalues in the context of max-plus algebra and forms the basis for many results. This paper aims at giving a complete proof of t...

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Bibliographic Details
Main Authors: van der Woude, J., Olsder, G.J.
Format: Conference Proceeding
Language:English
Subjects:
Algebra
Computer science
Eigenvalues and eigenfunctions
Jacobian matrices
Mathematics
Online Access:Request full text
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Summary:The so-called spectral theorem for square irreducibe matrices is well-known in the max-plus community. The theorem is a fundamental result concerning matrix powers and eigenvalues in the context of max-plus algebra and forms the basis for many results. This paper aims at giving a complete proof of the above spectral property in its full generality. In particular, the distinction will be highlighted between the graph cyclicity of a matrix (the cyclicity of the graph of the matrix) and the cyclicity of the matrix itself.
ISSN:0191-2216
DOI:10.1109/CDC.2005.1583423