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A Polynomial Approach to Linear Algebra (Universitext)by Paul A. Fuhrmann
Synopses & ReviewsPublisher Comments: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
Synopsis: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.
About the AuthorPaul Fuhrmann is a Professor in the Department of Mathematics at BenGurion University of the Negev.
Table of ContentsPreliminaries. 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.
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Related SubjectsScience and Mathematics » Mathematics » Algebra » Linear Algebra Science and Mathematics » Mathematics » Calculus » General Science and Mathematics » Mathematics » Systems Theory 

