Invariant Subspaces of Matrices with Applications

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.