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 EditionPreface to the First EditionIntroductionPart One: Fundamental Properties of Invariant Subspaces and Applications. Chapter 1: Invariant Subspaces: Definitions, Examples, and First PropertiesChapter 2: Jordan Form and Invariant SubspacesChapter 3: Coinvariant and Semiinvariant SubspacesChapter 4 Jordan Form for Extensions and CompletionsChapter 5: Applications to Matrix PolynomialsChapter 6: Invariant Subspaces for Transformations Between Different SpacesChapter 7: Rational Matrix FunctionsChapter 8: Linear SystemsPart Two: Algebraic Properties of Invariant Subspaces. Chapter 9: Commuting Matrices and Hyperinvariant SubspacesChapter 10: Description of Invariant Subspaces and Linear Transformation with the Same Invariant SubspacesChapter 11: Algebras of Matrices and Invariant SubspacesChapter 12: Real Linear TransformationsPart Three: Topological Properties of Invariant Subspaces and Stability. Chapter 13: The Metric Space of SubspacesChapter 14: The Metric Space of Invariant SubspacesChapter 15: Continuity and Stability of Invariant SubspacesChapter 16: Perturbations of Lattices of Invariant Subspaces with Restrictions on the Jordan StructureChapter 17: ApplicationsPart Four: Analytic Properties of Invariant Subspaces. Chapter 18: Analytic Families of SubspacesChapter 19: Jordan Form of Analytic Matrix FunctionsChapter 20: ApplicationsAppendix: List of Notations and ConventionsReferencesAuthor IndexSubject Index.