000			03077nam a22004815i 4500
001			978-1-4614-0338-8
003			DE-He213
005			20140220083238.0
007			cr nn 008mamaa
008			111121s2012 xxu| s |||| 0|eng d
020			_a9781461403388 _9978-1-4614-0338-8
024	7		_a10.1007/978-1-4614-0338-8 _2doi
050		4	_aQA184-205
072		7	_aPBF _2bicssc
072		7	_aMAT002050 _2bisacsh
082	0	4	_a512.5 _223
100	1		_aFuhrmann, Paul A. _eauthor.
245	1	2	_aA Polynomial Approach to Linear Algebra _h[electronic resource] / _cby Paul A. Fuhrmann.
264		1	_aNew York, NY : _bSpringer New York, _c2012.
300			_aXVI, 411p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_aPreliminaries -- 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			_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. 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	_aMathematics.
650		0	_aMatrix theory.
650		0	_aSystems theory.
650		0	_aMathematical optimization.
650	1	4	_aMathematics.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aSystems Theory, Control.
650	2	4	_aCalculus of Variations and Optimal Control; Optimization.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461403371
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-0338-8
912			_aZDB-2-SMA
999			_c100833 _d100833