000 03714nam a22005295i 4500
001 978-3-7643-8268-1
003 DE-He213
005 20180115171757.0
007 cr nn 008mamaa
008 100301s2008 sz | s |||| 0|eng d
020 _a9783764382681
_9978-3-7643-8268-1
024 7 _a10.1007/978-3-7643-8268-1
_2doi
050 4 _aQA329-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.724
_223
100 1 _aBart, Harm.
_eauthor.
245 1 0 _aFactorization of Matrix and Operator Functions: The State Space Method
_h[electronic resource] /
_cby Harm Bart, André C. M. Ran, Israel Gohberg, Marinus A. Kaashoek.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2008.
300 _aXII, 412 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOperator Theory: Advances and Applications, Linear Operators and Linear Systems ;
_v178
505 0 _aMotivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions.
520 _aThe present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces.
650 0 _aMathematics.
650 0 _aMatrix theory.
650 0 _aAlgebra.
650 0 _aOperator theory.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aOperator Theory.
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
650 2 4 _aNumber Theory.
700 1 _aRan, André C. M.
_eauthor.
700 1 _aGohberg, Israel.
_eauthor.
700 1 _aKaashoek, Marinus A.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764382674
830 0 _aOperator Theory: Advances and Applications, Linear Operators and Linear Systems ;
_v178
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7643-8268-1
912 _aZDB-2-SMA
999 _c372951
_d372951