Overview

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.

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9783764352592

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