A Polynomial Approach to Linear Algebra

Paul A. Fuhrmann

ISBN 10: 1461403375 / ISBN 13: 9781461403371

Published by Springer New York, Springer New York Nov 2011, 2011

About this Item

Neuware -A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra.This new edition has been updated throughout, in particular new sections have been added on rational interpolation, interpolation using H^{fty} functions, and tensor products of models.Review from first edition:¿¿the approach pursed by the author is of unconventional beauty and the material covered by the book is unique.¿ (Mathematical Reviews)Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 428 pp. Englisch.

Seller Inventory # 9781461403371

Bibliographic Details

• Title: A Polynomial Approach to Linear Algebra
• Publisher: Springer New York, Springer New York Nov 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 1461403375
• ISBN 13: 9781461403371
• Binding: Taschenbuch
• Edition: 1st Edition
• Condition: Neu
• Dimensions: 235W x 155H x 24D millimeters 235 millimeters width by 155 millimeters height by 24 millimeters depth
• Weight: 645 grams

About this title

Synopsis

A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra.

This new edition has been updated throughout, in particular new sections have been added on rational interpolation, interpolation using H^{\nfty} functions, and tensor products of models.

Review from first edition:

“…the approach pursed by the author is of unconventional beauty and the material covered by the book is unique.” (Mathematical Reviews)

About the Author

Paul Fuhrmann is a Professor in the Department of Mathematics at Ben-Gurion University of the Negev.