A Polynomial Approach to Linear Algebra

  • Paul A. Fuhrmann

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Paul A. Fuhrmann
    Pages 1-32
  3. Paul A. Fuhrmann
    Pages 33-53
  4. Paul A. Fuhrmann
    Pages 55-66
  5. Paul A. Fuhrmann
    Pages 67-95
  6. Paul A. Fuhrmann
    Pages 97-134
  7. Paul A. Fuhrmann
    Pages 135-159
  8. Paul A. Fuhrmann
    Pages 161-193
  9. Paul A. Fuhrmann
    Pages 195-278
  10. Paul A. Fuhrmann
    Pages 279-294
  11. Paul A. Fuhrmann
    Pages 295-324
  12. Paul A. Fuhrmann
    Pages 325-359
  13. Paul A. Fuhrmann
    Pages 361-402
  14. Back Matter
    Pages 403-411

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.

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 pursued by the author is of unconventional beauty and the material covered by the book is unique.” (Mathematical Reviews, A. Böttcher)

Keywords

Elements of Model reduction Linear Algebra Rational interpolation Tensor products and models

Authors and affiliations

  • Paul A. Fuhrmann
    • 1
  1. 1.Dept. Mathematics & Computer ScienceBen-Gurion University of the NegevBeer ShevaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0338-8
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-0337-1
  • Online ISBN 978-1-4614-0338-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book