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 becom...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Fuhrmann, Paul A. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2012.
Edición:2nd ed. 2012.
Colección:Universitext,
Temas:
Algebras, Linear.
System theory.
Control theory.
Mathematical optimization.
Calculus of variations.
Linear Algebra.
Systems Theory, Control .
Calculus of Variations and Optimization.
Acceso en línea:Texto Completo

MARC

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100 1 |a Fuhrmann, Paul A.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 2 |a A Polynomial Approach to Linear Algebra  |h [electronic resource] /  |c by Paul A. Fuhrmann. 
250 |a 2nd ed. 2012. 
264 1 |a New York, NY :  |b Springer New York :  |b Imprint: Springer,  |c 2012. 
300 |a XVI, 411 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a Universitext,  |x 2191-6675 
505 0 |a 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. 
520 |a 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. This new edition has been updated throughout, in particular new sections  have been added on rational interpolation, interpolation using H^{\nfty} functions, and tensor products of models. Review from first edition: "...the approach pursued by the author is of unconventional beauty and the material covered by the book is unique." (Mathematical Reviews, A. Böttcher). 
650 0 |a Algebras, Linear. 
650 0 |a System theory. 
650 0 |a Control theory. 
650 0 |a Mathematical optimization. 
650 0 |a Calculus of variations. 
650 1 4 |a Linear Algebra. 
650 2 4 |a Systems Theory, Control . 
650 2 4 |a Calculus of Variations and Optimization. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9781461403371 
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830 0 |a Universitext,  |x 2191-6675 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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