Invariant Subspaces of Matrices with Applications

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.