A Polynomial Approach to Linear Algebra

  • Paul A. Fuhrmann

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Paul A. Fuhrmann
    Pages 1-32
  3. Paul A. Fuhrmann
    Pages 33-52
  4. Paul A. Fuhrmann
    Pages 53-64
  5. Paul A. Fuhrmann
    Pages 65-96
  6. Paul A. Fuhrmann
    Pages 97-126
  7. Paul A. Fuhrmann
    Pages 127-149
  8. Paul A. Fuhrmann
    Pages 151-185
  9. Paul A. Fuhrmann
    Pages 187-249
  10. Paul A. Fuhrmann
    Pages 251-269
  11. Paul A. Fuhrmann
    Pages 271-303
  12. Paul A. Fuhrmann
    Pages 305-352
  13. Back Matter
    Pages 353-361

About this book

Introduction

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. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.

Keywords

algebra algorithms linear algebra operator theory quadratic form stability stability theory system transformation

Authors and affiliations

  • Paul A. Fuhrmann
    • 1
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-8734-1
  • Copyright Information Springer-Verlag New York, Inc. 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94643-6
  • Online ISBN 978-1-4419-8734-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book