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 sameperspective, 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 integralpart of linear algebra. New sections added on rational interpolation, interpolation using H^{ fty} functions and tensor products and models (scalar case).Review from first edition:. 'Fuhrmann has written an interesting book bring afresh approach to the structure theory of linear transformations and containing material that is not readily available elsewhere.'. (New Zealand Mathematical Society Newsletter, October 1999). Many additions including Rational interpolation, interpolation using H^{ fty} functions and tensor products and models (scalar case) Almost 100 new pages added Allows the reader to access ideas and results on the frontier of current research INDICE: Preliminaries. Linear Spaces. Determinants. Linear Transformations. The Shift Operator. Structure Theory of Linear Transformations. Inner Product Spaces. Quadratic Forms. Stability. Elements of System Theory. Hankel Norm Approximation.
- ISBN: 978-1-4614-0337-1
- Editorial: Springer New York
- Encuadernacion: Rústica
- Páginas: 440
- Fecha Publicación: 22/08/2011
- Nº Volúmenes: 1
- Idioma: Inglés
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