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  7. Partially Specified Matrices and Operators: Classification, Completion, Applications

Partially Specified Matrices and Operators: Classification, Completion, Applications

Israel Gohberg, Marinus Kaashoek, Frederik Van Schagen
Livre relié | Anglais | Operator Theory: Advances and Applications | n° 79
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Description

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.

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Auteur(s) :
Editeur:

Contenu

Nombre de pages :
368
Langue:
Anglais
Collection :
Tome:
n° 79

Caractéristiques

EAN:
9783764352592
Date de parution :
28-08-95
Format:
Livre relié
Format numérique:
Genaaid
Dimensions :
165 mm x 235 mm
Poids :
744 g

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