Overview
- Authors:
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Israel Gohberg
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School of Mathematical Sciences Raymon and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel
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Marinus A. Kaashoek
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Faculteit Wiskunde en Informatica, Vrije Universiteit Amsterdam, The Netherlands
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Frederik Schagen
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Faculteit Wiskunde en Informatica, Vrije Universiteit Amsterdam, The Netherlands
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Table of contents (16 chapters)
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Front Matter
Pages i-viii
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 1-3
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 5-23
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 25-38
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 39-57
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 59-82
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 83-105
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 107-111
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 113-138
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 139-142
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 143-176
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 177-188
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 189-216
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 217-242
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 243-266
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 267-276
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- Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen
Pages 277-295
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Back Matter
Pages 297-336
About this book
This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available.