000			a
999			_c29767 _d29767
008			191120b xxu||||| |||| 00| 0 eng d
020			_a9781461403371
082			_a512​.5 _bFUH
100			_aFuhrmann, Paul Abraham
245			_aPolynomial approach to linear algebra
260			_bSpringer _c2012 _aNew York
300			_axvi, 411 p. _bill. _c24 cm.
365			_b64.99 _cEUR _d82.00
504			_aIncludes bibliographical references and index.
520			_aA 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. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.
650			_aLinear Algebras
650			_aPolynomials
650			_aMathematics
650			_aAlgebra
650			_aSystem theory
650			_aCalculus of Variations and Optimal Control
650			_aMatrix theory
650			_aSystems Theory
650			_aOptimization
942			_2ddc _cBK