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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.
Israel Gohberg is Professor Emeritus at Tel-Aviv University and Free University of Amsterdam, and Dr. Honoris Causa at several European universities. He has contributed to the fields of functional analysis and operator theory, systems theory, matrix analysis and linear algebra, and computational techniques for integral equations and structured matrices. He has coauthored 25 books. Peter Lancaster is a Faculty Professor and Professor Emeritus at the University of Calgary and Honorary Research Fellow of the University of Manchester. He has published prolifically in matrix and operator theory and in many of their applications in numerical analysis, mechanics, and other fields. Leiba Rodman is Professor of Mathematics at the College of William and Mary and has done extensive work in matrix analysis, operator theory, and related fields. He has authored one book and coauthored six others.
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.
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- ID: 9780898716085
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