Invariant Subspaces of Matrices with Applications
Invariant Subspaces of Matrices with Applications
Israel Gohberg, Tel-Aviv University
Peter Lancaster, University of Calgary
Leiba Rodman, College of William and Mary, Virginia
Peter Lancaster, University of Calgary
Leiba Rodman, College of William and Mary, Virginia
March 2006
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Paperback
9780898716085
£97.00
GBPPaperback
This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions.
- Appropriate for students, instructors and researchers in applied linear algebra, linear systems theory, and signal processing
- Readers who have had undergraduate-level courses in linear theory and complex function theory will find this text readily accessible
- The mathematical foundations for linear systems theory are clearly presented, as well as a thorough treatment of analytic perturbation theory for matrix functions
Product details
March 2006Paperback
9780898716085
184 pages
228 × 152 × 27 mm
0.776kg
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
- Preface to the classics edition
- Preface to the first edition
- Introduction
- Part I. Fundamental Properties of Invariant Subspaces and Applications:
- 1. Invariant subspaces
- 2. Jordan form and invariant subspaces
- 3. Coinvariant and semiinvariant subspaces
- 4. Jordan form for extensions and completions
- 5. Applications to matrix polynomials
- 6. Invariant subspaces for transformations between different spaces
- 7. Rational matrix functions
- 8. Linear systems
- Part II. Algebraic Properties of Invariant Subspaces:
- 9. Commuting matrices and hyperinvariant subspaces
- 10. Description of invariant subspaces and linear transformation with the same invariant subspaces
- 11. Algebras of matrices and invariant subspaces
- 12. Real linear transformations
- Part III. Topological Properties of Invariant Subspaces and Stability:
- 13. The metric space of subspaces
- 14. The metric space of invariant subspaces
- 15. Continuity and stability of invariant subspaces
- 16. Perturbations of lattices of invariant subspaces with restrictions on the Jordan structure
- 17. Applications
- Part IV. Analytic Properties of Invariant Subspaces:
- 18. Analytic families of subspaces
- 19. Jordan form of analytic matrix functions
- 20. Applications
- Appendix
- References
- Author index
- Subject index.
