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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Vydané v:	Linear algebra and its applications Ročník 432; číslo 12; s. 3351 - 3360
Hlavný autor:	Wu, Huazhang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier Inc 01.07.2010 Elsevier
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Wu, Huazhang
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Keywords	Diagonal reduction Barnett-type formula Jacobson chain basis 15A57 Polynomial module Generalized polynomial Bezoutian Bézout idendity Matrix polynomial Factorization Generalized Companion matrix Vandermonde matrix
Language	English
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SubjectTerms	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
Title	Generalized polynomial Bezoutian with respect to a Jacobson chain basis over an arbitrary field
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