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 pursed by
the author is of unconventional beauty and the material covered by the book is unique.
(Mathematical Reviews)
