LEADER 04727nam 22007935 450 001 9910784771703321 005 20200630030204.0 010 $a1-281-14098-8 010 $a9786611140984 010 $a3-7643-8268-6 024 7 $a10.1007/978-3-7643-8268-1 035 $a(CKB)1000000000401439 035 $a(EBL)338235 035 $a(OCoLC)370725310 035 $a(SSID)ssj0000152855 035 $a(PQKBManifestationID)11165171 035 $a(PQKBTitleCode)TC0000152855 035 $a(PQKBWorkID)10392898 035 $a(PQKB)11649010 035 $a(DE-He213)978-3-7643-8268-1 035 $a(MiAaPQ)EBC338235 035 $a(MiAaPQ)EBC4975802 035 $a(Au-PeEL)EBL4975802 035 $a(CaONFJC)MIL114098 035 $a(OCoLC)1027172617 035 $a(PPN)123740258 035 $a(EXLCZ)991000000000401439 100 $a20100301d2008 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFactorization of Matrix and Operator Functions: The State Space Method$b[electronic resource] /$fby Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran 205 $a1st ed. 2008. 210 1$aBasel :$cBirkhäuser Basel :$cImprint: Birkhäuser,$d2008. 215 $a1 online resource (420 p.) 225 1 $aLinear Operators and Linear Systems,$x2504-3609 ;$v178 300 $aDescription based upon print version of record. 311 $a3-7643-8267-8 327 $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. 330 $aThe present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces. 410 0$aLinear Operators and Linear Systems,$x2504-3609 ;$v178 606 $aOperator theory 606 $aMatrix theory 606 $aAlgebra 606 $aNumber theory 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aOperator theory. 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aNumber theory. 615 14$aOperator Theory. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aNumber Theory. 676 $a512.9434 700 $aBart$b Harm$4aut$4http://id.loc.gov/vocabulary/relators/aut$054313 702 $aGohberg$b Israel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKaashoek$b Marinus A$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRan$b André C.M$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784771703321 996 $aFactorization of Matrix and Operator Functions: The State Space Method$93720110 997 $aUNINA