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Invariant Subspaces of Matrices with Applications

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By Israel Gohberg, Peter Lancaster, and Leiba Rodman


2006 / xxii+692 pages / Softcover / ISBN: 978-0-898716-08-5 / List Price $130.00 / SIAM Member Price $91.00 / Order Code CL51

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.

This book is appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex function theory.

Preface to the Classics Edition; Preface to the First Edition; Introduction; Part One: Fundamental Properties of Invariant Subspaces and Applications. Chapter 1: Invariant Subspaces: Definitions, Examples, and First Properties; Chapter 2: Jordan Form and Invariant Subspaces; Chapter 3: Coinvariant and Semiinvariant Subspaces; Chapter 4 Jordan Form for Extensions and Completions; Chapter 5: Applications to Matrix Polynomials; Chapter 6: Invariant Subspaces for Transformations Between Different Spaces; Chapter 7: Rational Matrix Functions; Chapter 8: Linear Systems; Part Two: Algebraic Properties of Invariant Subspaces. Chapter 9: Commuting Matrices and Hyperinvariant Subspaces; Chapter 10: Description of Invariant Subspaces and Linear Transformation with the Same Invariant Subspaces; Chapter 11: Algebras of Matrices and Invariant Subspaces; Chapter 12: Real Linear Transformations; Part Three: Topological Properties of Invariant Subspaces and Stability. Chapter 13: The Metric Space of Subspaces; Chapter 14: The Metric Space of Invariant Subspaces; Chapter 15: Continuity and Stability of Invariant Subspaces; Chapter 16: Perturbations of Lattices of Invariant Subspaces with Restrictions on the Jordan Structure; Chapter 17: Applications; Part Four: Analytic Properties of Invariant Subspaces. Chapter 18: Analytic Families of Subspaces; Chapter 19: Jordan Form of Analytic Matrix Functions; Chapter 20: Applications; Appendix: List of Notations and Conventions; References; Author Index; Subject Index.

About the Authors
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.

ISBN: 9780898716085

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