A Polynomial Approach to Linear Algebra
(Sprache: Englisch)
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...
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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.
Klappentext zu „A Polynomial Approach to Linear Algebra “
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.
Inhaltsverzeichnis zu „A Polynomial Approach to Linear Algebra “
1 Preliminaries2 Linear Spaces
3 Determinants
4 Linear Transformations
5 The Shift Operator
6 Structure Theory of Linear Transformations
7 Inner Product Spaces
8 Quadratic Forms
9 Stability
10 Elements of System Theory
11 Hankel Norm Approximation
Autoren-Porträt von Paul A. Fuhrmann
Paul A. Fuhrmann is a Professorin the Department of Mathematics at Ben-Gurion University of the Negev.
Bibliographische Angaben
- Autor: Paul A. Fuhrmann
- 1996, XIII, 360 Seiten, Maße: 15,6 x 23,4 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 0387946438
- ISBN-13: 9780387946436
Sprache:
Englisch
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