Generalized polynomial Bezoutian with respect to a Jacobson chain basis over an arbitrary field

We introduce a so-called generalized polynomial Bezoutian with respect to a Jacobson chain basis over an arbitrary field. Some characterization of this kind of matrix, such as the Barnett-type factorization and the intertwining relation with generalized hypercompanion matrix, are obtained. The diago...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 432; no. 12; pp. 3351 - 3360
Main Author: Wu, Huazhang
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.07.2010
Elsevier
Subjects:
Algebra
Barnett-type formula
Diagonal reduction
Exact sciences and technology
Field theory and polynomials
Generalized polynomial Bezoutian
Jacobson chain basis
Linear and multilinear algebra, matrix theory
Mathematics
Polynomial module
Sciences and techniques of general use
Diagonal reduction
Barnett-type formula
Jacobson chain basis
15A57
Polynomial module
Generalized polynomial Bezoutian
Bézout idendity
Matrix polynomial
Factorization
Generalized
Companion matrix
Vandermonde matrix
ISSN:0024-3795
Online Access:Get full text
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Summary:We introduce a so-called generalized polynomial Bezoutian with respect to a Jacobson chain basis over an arbitrary field. Some characterization of this kind of matrix, such as the Barnett-type factorization and the intertwining relation with generalized hypercompanion matrix, are obtained. The diagonal reduction formula via the generalized confluent Vandermonde matrix similar to that of classical Bezoutian is presented. The method used is based on polynomial module and operator representation.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.01.032