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

07/02/2020

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by   A. C. M. Ran, et al.

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General properties of eigenvalues of A+τ uv^* as functions of τ∈ or τ∈ or τ=^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.