Title: A min-plus analogue of the Jordan canonical form associated with the basis of the generalized eigenspace
Abstract: In this paper, we investigate a min-plus analogue of Jordan canonical forms of matrices. We first define the generalized eigenvector of a min-plus matrix A as an eigenvector of the kth power of A for some integer k. As in the conventional algebra, we consider a transformation matrix consisting of the basis of the generalized eigenspace. Then, we call a block diagonal matrix obtained from such transformation matrix a Jordan canonical form. In min-plus algebra, however, not all square matrices have Jordan canonical forms. We derive a necessary and sufficient condition of matrices having those in terms of graph theory.
Publication Year: 2019
Publication Date: 2019-12-06
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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