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.
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Book Description
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Book Description
This unique book addresses advanced linear algebra using invariant subspaces as the central notion and main tool. It comprehensively covers geometrical, algebraic, topological, and analytic properties of invariant subspaces, laying clear mathematical foundations for linear systems theory with a thorough treatment of analytic perturbation theory for matrix functions.
From the Publisher
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.
--This text refers to an out of print or unavailable edition of this title.
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First Sentence:
Invariant subspaces are a central notion of linear algebra. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
null kernel pair, linear matrix polynomials, monic matrix polynomials, analytic extendability, linear fractional decompositions, partial multiplicities, minimal linear fractional decomposition, right standard pair, minimal column indices, subspace tit, minimal row indices, angular with respect, simple rectifiable contour, coinvariant subspaces, left standard pair, spectral assignment problem, rational matrix functions, same invariant subspaces, stable invariant subspaces, analytic vector functions, minimal factorization, spectral invariant subspace, algebraic branch points, scalar rational functions, hyperinvariant subspaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Solve Exercise, Use Exercise, Hence Ker, Hence Span New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Invariant subspaces are a central notion of linear algebra. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
null kernel pair, linear matrix polynomials, monic matrix polynomials, analytic extendability, linear fractional decompositions, partial multiplicities, minimal linear fractional decomposition, right standard pair, minimal column indices, subspace tit, minimal row indices, angular with respect, simple rectifiable contour, coinvariant subspaces, left standard pair, spectral assignment problem, rational matrix functions, same invariant subspaces, stable invariant subspaces, analytic vector functions, minimal factorization, spectral invariant subspace, algebraic branch points, scalar rational functions, hyperinvariant subspaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Solve Exercise, Use Exercise, Hence Ker, Hence Span New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 68
books:
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34
books
cite this book:
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- Ordinary Differential Equations (Classics in Applied Mathematics) by George F. Carrier in Front Matter (1), and Front Matter (2)
- Matrix Polynomials (Computer Science and Applied Mathematics) by I. Gohberg in Back Matter (1), and Back Matter (2)
- Invariant Subspaces (Dover Books on Mathematics) by Heydar Radjavi on page 385, and Back Matter
- Perturbation Theory for Linear Operators (Classics in Mathematics) by Tosio Kato in Back Matter
- Differential Analysis on Complex Manifolds (Graduate Texts in Mathematics, Vol 65) by Raymond O'Neil Wells in Back Matter
See all 68 books this book cites
- The Gohberg Anniversary Collection Vol 1: The Calgary Conference and Matrix Theory Papers (Operator Theory: Advances and Applications v40) (v. 1) by Seymour Goldberg on page 85, page 149, and page 434
- Operator Theory and Analysis: The M.A. Kaashoek Anniversary Volume, Workshop in Amsterdam, November 12-14, 1997 (Operator Theory: Advances and Applications) by H. Bart on page 245, and page 382
- Notes on Fermat's Last Theorem (Canadian Mathematical Society Series of Monographs and Advanced Texts) by Alf J. van der Poorten in Front Matter
- Gauss and Jacobi Sums (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Bruce C. Berndt in Back Matter
- Topics in Matrix Analysis by Roger A. Horn in Back Matter
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