Factorization of Matrix and Operator Functions: The State Space Method

The 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 co...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Bart, Harm (Author), Gohberg, Israel (Author), Kaashoek, Marinus A. (Author), Ran, André C.M (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2008.
Edition:1st ed. 2008.
Series:Linear Operators and Linear Systems, 178
Subjects:
Operator theory.
Algebras, Linear.
Number theory.
Operator Theory.
Linear Algebra.
Number Theory.
Online Access:Texto Completo

MARC

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100 1 |a Bart, Harm.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Factorization of Matrix and Operator Functions: The State Space Method  |h [electronic resource] /  |c by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran. 
250 |a 1st ed. 2008. 
264 1 |a Basel :  |b Birkhäuser Basel :  |b Imprint: Birkhäuser,  |c 2008. 
300 |a XII, 412 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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490 1 |a Linear Operators and Linear Systems,  |x 2504-3617 ;  |v 178 
505 0 |a Motivating 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 |a The 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 |a Operator theory. 
650 0 |a Algebras, Linear. 
650 0 |a Number theory. 
650 1 4 |a Operator Theory. 
650 2 4 |a Linear Algebra. 
650 2 4 |a Number Theory. 
700 1 |a Gohberg, Israel.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Kaashoek, Marinus A.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Ran, André C.M.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783764391911 
776 0 8 |i Printed edition:  |z 9783764382674 
830 0 |a Linear Operators and Linear Systems,  |x 2504-3617 ;  |v 178 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-7643-8268-1  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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