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Invariant subspaces of matrices with applications / Israel Gohberg, Peter Lancaster, Leiba Rodman.
- Format:
- Book
- Author/Creator:
- Gohberg, I. (Israel), 1928-
- Series:
- Classics in applied mathematics ; 51.
- Classics in applied mathematics ; 51
- Language:
- English
- Subjects (All):
- Invariant subspaces.
- Matrices.
- Physical Description:
- 1 electronic text (xxi, 692 p.) : digital file.
- Place of Publication:
- Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2006.
- Language Note:
- English
- System Details:
- Mode of access: World Wide Web.
- System requirements: Adobe Acrobat Reader.
- Summary:
- 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. Audience: appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex function theory.
- Contents:
- Invariant subspaces: definitions, examples, and first properties
- Jordan form and invariant subspaces
- Coinvariant and semiinvariant subspaces
- Jordan form for extensions and completions
- Applications to matrix polynomials
- Invariant subspaces for transformations between different spaces
- Rational matrix functions
- Linear systems
- Commuting matrices and hyperinvariant subspaces
- Description of invariant subspaces and linear transformation with the same invariant subspaces
- Algebras of matrices and invariant subspaces
- Real linear transformations
- 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 on the Jordan structure
- Applications
- Analytic families of subspaces
- Jordan form of analytic matrix functions
- Applications.
- Notes:
- Originally published: New York : Wiley, c1986, in series: Canadian Mathematical Society series of monographs and advanced texts.
- Includes bibliographical references (p. 683-686) and indexes.
- Description based on title page of print version.
- ISBN:
- 0-89871-909-7
- Publisher Number:
- CL51 siam
- CL51 SIAM
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