Invariant Subspaces of Matrices with Applications

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.

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.

This unique book addresses advanced linear algebra using invariant subspaces as the central notion and main tool. It comprehensively covers geometrical, algebraic, topological, and analytic properties of invariant subspaces, laying clear mathematical foundations for linear systems theory with a thorough treatment of analytic perturbation theory for matrix functions.