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Field name	Details
Dewey Class	512.5
Title	A Polynomial Approach to Linear Algebra ([Ebook]) / by Paul A. Fuhrmann.
Author	Fuhrmann, Paul Abraham
Other name(s)	SpringerLink (Online service)
Edition statement	2nd edition
Publication	New York, NY : Springer , 2012.
Physical Details	XVI, 411 pages : online resource.
Series	Universitext 0172-5939
ISBN	9781461403388
Summary Note	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 sectionsÂ have been added on rational interpolation, interpolation using H {\nfty} functions, and tensor products of models. Review from first edition: ââ¦the approach pursued by the author is of unconventional beauty and the material covered by the book is unique.â (Mathematical Reviews, A. BÃ¶ttcher):
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4614-0338-8
Links to Related Works	Subject References: Calculus of variations and optimal control; optimization . Linear and Multilinear Algebras, Matrix Theory . Mathematical optimization . Mathematics . Matrix theory . Systems theory . Systems Theory, Control . Authors: Fuhrmann, Paul Abraham . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 512.5 . 512.5 (DDC 23) .

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A Polynomial Approach to Linear Algebra

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