Partially Specified Matrices and Operators: Classification, Completion, Applications

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This book explores a new direction in linear algebra and operator theory dealing 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 problem of classification of partially specified matrices, and the results here may be seen as a far reaching generalization of the Jordan canonical form. ...
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1995 Hard cover New Sewn binding. Cloth over boards. 333 p. Respiratory Pharmacology and Pharmacotherapy, 79. Audience: General/trade. BRAND NEW. gift quality. NO DJ (as issued)

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Overview

This book explores a new direction in linear algebra and operator theory dealing 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 problem of classification of partially specified matrices, and the results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is the eigenvalue completion problem, which asks for a description of 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 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 book will appeal to a wide group of mathematicians and engineers. Much of the material can be used in advanced courses in matrix and operator theory.
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Editorial Reviews

Booknews
Explores a new direction in linear algebra and operator theory dealing with the invariants of partially specified matrices and operators, and the spectral analysis of their completions. The approach revolves around two problems: the classification of partially specified matrices, the solution to which is a broad generalization of the Jordan canonical form; and an eigenvalue completion problem that asks for a description of all possible eigenvalues and their multiplicities of the matrices, obtained by filling in the unspecified entries. Addressed to mathematicians and engineers in a wide range of fields, and suitable as a text for a course in matrix and operator theory for advanced students who are familiar with linear algebra. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Introduction
I Main problems and motivation
II Elementary operations on blocks
III Full length blocks
IV The eigenvalue completion problem for full length blocks
V Full width blocks
VI Principal blocks
VII General blocks
VIII Off-diagonal blocks
IX Connections with linear systems
X Applications to matrix polynomials
XI Applications to rational matrix functions
XII Infinite dimensional operator blocks
XIII Factorization of operator polynomials
XIV Factorization of analytic operator functions
XV Eigenvalue completion problems for triangular matrices
App. A.1 Root functions of regular analytic matrix functions
App. A.2 Right Jordan pairs of regular analytic matrix functions
App. A.3 Left Jordan pairs
App. A.4 Jordan pairs and Laurent principal parts
App. A.5 Global spectral data for regular analytic matrix functions
Bibliography
List of notations
Index
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