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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Polynomial Matrix and Valuated Matroid
verfasst von : Kazuo Murota
Erschienen in: Matrices and Matroids for Systems Analysis
Verlag: Springer Berlin Heidelberg
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Matrices consisting of polynomials or rational functions play fundamental roles in various branches in engineering. Combinatorial properties of polynomial matrices are abstracted in the language of valuated matroids. This chapter is mostly devoted to an exposition of the theory of valuated matroids, whereas the first section describes a number of canonical forms of polynomial/rational matrices that are amenable to combinatorial methods of analysis to be explained in Chap. 6.