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Matrix extensions and eigenvalue completions, the generic case. (English) Zbl 0891.15004
Given an \(n\times n\) matrix \(A\), this paper concerns conditions under which the mapping from a certain subspace of the \(n\times n\) matrices \(L\) to the polynomials det\((sI-A-L)\) is “almost onto”. The main result includes several important classical theorems as special cases. A good introduction to some of the ideas considered here is given in the monograph of I. Gohberg, M. A. Kaashoek and F. van Schagen, Partially specified matrices and operators: classification, completion, applications (1995; Zbl 0832.15004).

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
93B60 Eigenvalue problems
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