Factorization of Matix and Operator Functions
, by Bart, Harm; Gohberg, Israel; Kaashoek, Marinus A.; Ran, Andre C. M.Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
- ISBN: 9783764382674 | 3764382678
- Cover: Hardcover
- Copyright: 2/3/2008
The present book deals with 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, 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. This principle allows one to deal with various factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, degree one factorizations and others. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.