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arXiv · 2007.01188

Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices

A. C. M. Ran·Michal Wojtylak
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Abstract

General properties of eigenvalues of $A+τuv^*$ as functions of $τ\in\Comp$ or $τ\in\Real$ or $τ=\e^{\iiθ}$ 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 $τ\to\infty$ 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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A. C. M. Ran, Michal Wojtylak. 2020-07-02. Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices. https://arxiv.org/abs/2007.01188

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