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Eigenspace of a circulant max-min matrix. (English) Zbl 1206.15008

The min-max algebra considered in the paper is a linearly ordered set \(\mathcal B\) equipped with binary operations \(a\oplus b=\max\{a,b\}\) and \(a\otimes b=\min\{a,b\}\). The authors deal with circulant matrices \(A\in\mathcal B^{n\times n}\) and its eigenvectors \(x\in\mathcal B^{n\times1}\) (i.e. \(Ax=x\)). Some sufficient and/or necessary conditions for \(x\) to be an eigenvector of \(A\) are given. The results are illustrated on some examples for \(n=12\), and a set \(\mathcal B\) of positive integers with the natural order.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15A80 Max-plus and related algebras
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References:

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