Abstract
As in [N], [LN] the Newton diagram is used in order to get information about the first terms of the Puiseux expansions of the eigenvalues λ(ε) of the perturbed matrix pencilT(λ, ε)=A(λ)+B(λ, ε) in the neighbourhood of an unperturbed eigenvalue λ(∈) ofA(λ). In fact sufficient conditions are given which assure that the orders of these first terms correspond to the partial multiplicities of the eigenvalue λ0 ofA(λ).
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References
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[N] Najman, B., Remarks on the perturbation of analytic matrix functions, Integral Equations Operator Theory 9 (1986), 592–599.
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Langer, H., Najman, B. Remarks on the perturbation of analytic matrix functions III. Integr equ oper theory 15, 796–806 (1992). https://doi.org/10.1007/BF01200701
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DOI: https://doi.org/10.1007/BF01200701