Invariant subspaces of matrices with applications

Author(s)

• Lancaster, Peter
• Gohberg, Israel
• Rodman, L.

Bibliographic Information

Invariant subspaces of matrices with applications

I. Gohberg, P. Lancaster, L. Rodman

（Canadian Mathematical Society series of monographs and advanced texts）

Wiley, c1986

Description and Table of Contents

Description

This unique treatment of linear algebra 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. Also presented is an algebraic treatment of control and systems theories. Written by a world-famous expert, this text contains material not previously published, and includes numerous exercises.

Table of Contents

• 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.

by "Nielsen BookData"

Details

• NCID: BA00266362
• ISBN:
  • 0471842605
• LCCN: 86011091
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York
• Pages/Volumes: xv, 692 p.
• Size: 24 cm
• Classification:
  • LCC : QA322
  • DC19 : 515.7/246
  • NDC8 : 415.5
• Subject Headings:
  • LCSH : Invariant subspaces
  • LCSH : Matrices
• Parent Bibliography ID:
  • BA00266395