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Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices

General properties of eigenvalues of A + τ u v ∗ as functions of τ ∈ C or τ ∈ R or τ = e i θ on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with τ → ∞ are discussed in detail....

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Published in:Complex analysis and operator theory 2021-04, Vol.15 (3), Article 44
Main Authors: Ran, André C. M., Wojtylak, Michał
Format: Article
Language:English
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Summary:General properties of eigenvalues of A + τ u v ∗ as functions of τ ∈ C or τ ∈ R or τ = e i θ on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with τ → ∞ are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex H -selfadjoint and real J -Hamiltonian.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-021-01094-7