Graph-theoretically determined Jordan-block-size structure of regular matrix pencils
type: Item
instance of: scholarly article
title: Graph-theoretically determined Jordan-block-size structure of regular matrix pencils
zbMATH Open document ID: 0883.15005
DOI: 10.1016/S0024-3795(96)00589-7
author: Klaus Röbenack
author: Kurt J. Reinschke
published in: Linear Algebra and its Applications
publication date: 1998-03-22T00:00:00Z
review text: The sizes of Jordan blocks of regular matrix pencils are investigated by means of a one-to-one correspondence between a matrix pencil \((\lambda E+\mu A)\) and a weighted digraph \(G(E,A)\). Based on the relationship between determinantal divisors of a pencil and spanning-cycle families of the associated digraph \(G(E,A)\), the Jordan-block-size structure is determined graph-theoretically. For classes of structurally equivalent matrix pencils defined by a pair of structure matrices \([E,A]\), the generic Jordan block sizes corresponding to the characteristic roots at zero and at infinity can be obtained from the unweighted digraph \(G([E],[A])\). Eigenvalues of matrices are discussed as special cases.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1067957
zbMATH Keywords: eigenvalues
zbMATH Keywords: Jordan blocks
zbMATH Keywords: matrix pencils
zbMATH Keywords: weighted digraph
zbMATH Keywords: determinantal divisors
zbMATH Keywords: spanning-cycle
reviewed by: Giacomo Bonanno
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1067957