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Invariant Subspaces of Matrices with Applications

Invariant Subspaces of Matrices with Applications

£97.00

Part of Classics in Applied Mathematics

  • Date Published: March 2006
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716085

£ 97.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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  • 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
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    Product details

    • Date Published: March 2006
    • format: Paperback
    • isbn: 9780898716085
    • length: 184 pages
    • dimensions: 228 x 152 x 27 mm
    • weight: 0.776kg
    • availability: 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.

  • Authors

    Israel Gohberg, Tel-Aviv University

    Peter Lancaster, University of Calgary

    Leiba Rodman, College of William and Mary, Virginia

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