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A unique treatment of linear algebra which establishes the central role of invariant subspaces in the analysis of linear transformation. Incorporating the newest developments in linear algebra stimulated by linear systems theory, it gives a comprehensive view of geometrical, algebraic, topological, and analytical properties of invariant subspaces, with an emphasis on applications to matrix polynomials, rational matrix functions, linear systems, and matrix quadratic equations. Presents an algebraic treatment of control and systems theories. Written by a world-famous expert, this text contains material not previously published. Includes numerous exercises.
|Series:||Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts Series , #6|
|Product dimensions:||6.50(w) x 9.61(h) x 1.61(d)|
Table of Contents
Partial table of contents:
FUNDAMENTAL PROPERTIES OF INVARIANT SUBSPACES AND APPLICATIONS.
Invariant Subspaces: Definition, Examples and First Properties.
Jordan Form and Invariant Subspaces.
Coinvariant and Semiinvariant Subspaces.
Jordan Form for Extensions and Completions.
ALGEBRAIC PROPERITES OF 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.
ANALYTIC PROPERTIES OF INVARIANT SUBSPACES.
Analytic Families of Subspaces.
Jordan Form of Analytic Matrix Functions.
List of Notations and Conventions.