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.

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" may belong to another edition of this title.

Store Description

Seit �ber 30 Jahren handeln wir mit B�chern. Begonnen hat alles als kleiner Fachbuchhandel in Berlin. Heute sind wir spezialisiert auf den An- und Verkauf gebrauchter B�cher. Noch immer liegt unser Fokus dabei auf den Kategorien: Fachbuch und englischsprachige Literatur. Hinzu kommen B�cher aus allen anderen Genres, wie Belletristik, Biografien oder Kinderb�cher. Unser oberstes Ziel ist dabei die Weiterverwendung von Dingen und die Schonung von Ressourcen. Neben dem Ankauf von privaten B�chern oder Haushaltsaufl�sungen kaufen wir bundesweit komplette Bibliotheken und Buchbest�nde von Institutionen auf, um diese nachhaltig ein weiteres Mal auf den Markt zu bringen. Parallel dazu bietet Buchpark die M�glichkeit, gro�e Mengen einzulagern. Ganze Bibliotheken und umfangreiche Buchbest�nde werden von uns professionell auf Qualit�tsmerkmale hin untersucht und sorgf�ltig f�r den Onlinehandel aufbereitet. Wir schenken B�chern ein zweites Leben.

Visit Seller's Storefront