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A Polynomial Approach to Linear Algebra

  • Textbook
  • © 1996

Overview

Authors:
  1. Paul A. Fuhrmann

    1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

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Part of the book series: Universitext (UTX)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Preliminaries

    • Paul A. Fuhrmann
    Pages 1-32

  3. Linear Spaces

    • Paul A. Fuhrmann
    Pages 33-52

  4. Determinants

    • Paul A. Fuhrmann
    Pages 53-64

  5. Linear Transformations

    • Paul A. Fuhrmann
    Pages 65-96

  6. The Shift Operator

    • Paul A. Fuhrmann
    Pages 97-126

  7. Structure Theory of Linear Transformations

    • Paul A. Fuhrmann
    Pages 127-149

  8. Inner Product Spaces

    • Paul A. Fuhrmann
    Pages 151-185

  9. Quadratic Forms

    • Paul A. Fuhrmann
    Pages 187-249

  10. Stability

    • Paul A. Fuhrmann
    Pages 251-269

  11. Elements of System Theory

    • Paul A. Fuhrmann
    Pages 271-303

  12. Hankel Norm Approximation

    • Paul A. Fuhrmann
    Pages 305-352

  13. Back Matter

    Pages 353-361
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Paul A. Fuhrmann

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