Factorization of Matrix and Operator Functions: The State Space Method
Bart, Harm.
creator
author.
Ran, AndrĂ© C. M.
author.
Gohberg, Israel.
author.
Kaashoek, Marinus A.
author.
SpringerLink (Online service)
text
sz
2008
monographic
eng
access
XII, 412 p. online resource.
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.
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.
by Harm Bart, AndrĂ© C. M. Ran, Israel Gohberg, Marinus A. Kaashoek.
Mathematics
Matrix theory
Algebra
Operator theory
Number theory
Mathematics
Operator Theory
Linear and Multilinear Algebras, Matrix Theory
Number Theory
QA329-329.9
515.724
Springer eBooks
Operator Theory: Advances and Applications, Linear Operators and Linear Systems ; 178
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http://dx.doi.org/10.1007/978-3-7643-8268-1
http://dx.doi.org/10.1007/978-3-7643-8268-1
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