000  03714nam a22005295i 4500  

001  9783764382681  
003  DEHe213  
005  20180115171757.0  
007  cr nn 008mamaa  
008  100301s2008 sz  s  0eng d  
020 
_a9783764382681 _99783764382681 

024  7 
_a10.1007/9783764382681 _2doi 

050  4  _aQA329329.9  
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 PoleZero 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 nonselfadjoint 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 inputoutput 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 nonminimal factorizations, pseudocanonical 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/10.1007/9783764382681 
912  _aZDB2SMA  
999 
_c372951 _d372951 