Advertisement

Partially Specified Matrices and Operators: Classification, Completion, Applications

  • Israel Gohberg
  • Marinus A. Kaashoek
  • Frederik van Schagen

Part of the Operator Theory Advances and Applications book series (OT, volume 79)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 1-3
  3. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 5-23
  4. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 25-38
  5. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 39-57
  6. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 59-82
  7. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 83-105
  8. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 107-111
  9. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 113-138
  10. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 139-142
  11. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 143-176
  12. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 177-188
  13. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 189-216
  14. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 217-242
  15. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 243-266
  16. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 267-276
  17. Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
    Pages 277-295
  18. Back Matter
    Pages 297-336

About this book

Introduction

This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non­ everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available.

Keywords

Eigenvalue Interpolation Matrix Matrix Theory algebra analysis linear algebra operator operator theory systems theory

Authors and affiliations

  • Israel Gohberg
    • 1
  • Marinus A. Kaashoek
    • 2
  • Frederik van Schagen
    • 2
  1. 1.School of Mathematical Sciences Raymon and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  2. 2.Faculteit Wiskunde en InformaticaVrije Universiteit AmsterdamThe Netherlands

Bibliographic information

Industry Sectors
Finance, Business & Banking
Telecommunications