A Polynomial Approach to Linear Algebra
Paul A. Fuhrmann(Author)
Springer (Publisher)
1st Edition
Published on 20. June 1996
Book
Paperback/Softback
XIII, 361 pages
978-0-387-94643-6 (ISBN)
Article exhausted; check for reprint
Description
"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.
More details
Series
Language
English
Place of publication
New York
United States
Target group
College/higher education
Professional and scholarly
Professional/practitioner
Product notice
Paperback (trade)
Illustrations
black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 19 mm
Weight
1170 gr
ISBN-13
978-0-387-94643-6 (9780387946436)
DOI
10.1007/978-1-4419-8734-1
Schweitzer Classification
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Paul A. Fuhrmann
A Polynomial Approach to Linear Algebra
Book
11/2011
2nd Edition
Springer
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Paul A. Fuhrmann
A Polynomial Approach to Linear Algebra
E-Book
10/2012
Springer
€82.38
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Content
1 Preliminaries 2 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