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A polynomial approach to linear algebra

Author: Paul Abraham Fuhrmann
Publisher: New York : Springer, ©1996.
Series: Universitext.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Biased towards functional methods, this work presents a polynomial approach to Linear Algebra. Using the shift operator as a central object it makes linear algebra a suitable introduction to other  Read more...

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Genre/Form: Matériel didactique
Document Type: Book
All Authors / Contributors: Paul Abraham Fuhrmann
ISBN: 0387946438 9780387946436
OCLC Number: 301554139
Description: xiii, 360 p.
Contents: 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.
Series Title: Universitext.
Responsibility: P.A. Fuhrmann.
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