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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 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 1661-8254 1661-8262 |
DOI: | 10.1007/s11785-021-01094-7 |