Factorization of Matrix and Operator Functions: The State Space Method

  • Harm Bart
  • André C. M. Ran
  • Israel Gohberg
  • Marinus A. Kaashoek

Part of the Operator Theory: Advances and Applications book series (OT, volume 178)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. Pages 1-3
  3. Motivating Problems, Systems and Realizations

  4. Minimal Realization and Minimal Factorization

  5. Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling

  6. Stability of Factorization and of Invariant Subspaces

    1. Front Matter
      Pages 317-317
    2. Pages 339-373
  7. Back Matter
    Pages 393-409

About this book


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.


Matrix convolution factorization matrix function state space method

Authors and affiliations

  • Harm Bart
    • 1
  • André C. M. Ran
    • 2
  • Israel Gohberg
    • 3
  • Marinus A. Kaashoek
    • 2
  1. 1.Econometrisch InstituutErasmus Universiteit RotterdamRotterdamThe Netherlands
  2. 2.Department of Mathematics, FEWVrije Universiteit AmsterdamAmsterdamThe Netherlands
  3. 3.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael

Bibliographic information