Partially Specified Matrices and Operators: Classification, Completion, Applications: 79 (Operator Theory: Advances and Applications, 79) - Hardcover

Gohberg, Israel; Kaashoek, Marinus; Van Schagen, Frederik

Hardcover

ISBN 10: 3764352590 ISBN 13: 9783764352592

Publisher: Birkhauser Verlag AG, 1995

Synopsis

This text explores a 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 centres 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 problems. This text should appeal to a wide group of mathematicians and engineers, and much of the material can be used in advanced courses in matrix and operator theory.

About this title

Synopsis

This text explores a 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 centres 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 problems.

This text should appeal to a wide group of mathematicians and engineers, and much of the material can be used in advanced courses in matrix and operator theory.

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 1995
• Language: English
• ISBN 10: 3764352590
• ISBN 13: 9783764352592
• Binding: Hardcover
• Number of pages: 368