Factorization of Matrix and Operator Functions

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Oktober 2007



This book delineates the various types of 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, and the theory of job scheduling in operations research. The book presents 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.


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.
EAN: 9783764382674
ISBN: 3764382678
Untertitel: The State Space Method. 'Operator Theory: Advances and Applications'. 2008. Auflage. Illustrations. Book. Sprache: Englisch.
Verlag: Springer Basel AG
Erscheinungsdatum: Oktober 2007
Seitenanzahl: XII
Format: gebunden
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