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On the problem \(Ax= \lambda Bx\) in max algebra: Every system of intervals is a spectrum. (English) Zbl 1248.15023

In max algebras, a very important problem is the eigenproblem. There exist efficient algorithms for computing both eigenvalues and eigenvectors. The present paper deals with the two-sided generalized eigenproblem over a max algebra which does not seem to be well-known unlike the eigenproblem. The spectrum may include intervals and it is proved that any finite system of real intervals can be represented as spectrum of this eigenproblem.

MSC:

15A80 Max-plus and related algebras
15A18 Eigenvalues, singular values, and eigenvectors
15A22 Matrix pencils
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