Remarks on the perturbation of analytic matrix functions III

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).