Invariant Subspaces of Matrices with Applications 论文

摘要

FUNDAMENTAL PROPERTIES OF INVARIANT SUBSPACES AND APPLICATIONS: Invariant Subspaces: Definition, Examples and First Properties Jordan Form and Invariant Subspaces Coinvariant and Semi-invariant Subspaces Jordan Form for Extensions and Completions Applications to Matrix Polynomials Invariant Subspaces for Transformations between Different Spaces Rational Matrix Functions Linear Systems ALGEBRAIC PROPERTIES OF INVARIANT SUBSPACES: Commuting Matrices and Hyperinvariant Subspaces Description of Invariant Subspaces and Linear Transformations with the Same Invariant Subspaces Algebras of Matrices and Invariant Subspaces Real Linear Transformations TOPOLOGICAL PROPERTIES OF INVARIANT SUBSPACES AND STABILITY: The Metric Space of Subspaces The Metric Space of Invariant Subspaces Continuity and Stability of Invariant Subspaces Perturbations of Lattices of Invariant Subspaces with Restrictions Applications ANALYTIC PROPERTIES OF INVARIANT SUBSPACES: Analytic Families of Subspaces Jordan Form of Analytic Matrix Functions Applications Appendix List of Notations and Conventions References.