Sensitivity analysis of multiple eigenvalues and associated eigenvectors of quadratic eigenproblem

The article is focused on the sensitivity of eigenvalues and eigenvectors in a quadratic eigenvalue problem with real matrices defining the problem under consideration and under the strong assumption that these matrices form a non-defective operator.The particular interest is the case of multiple eigenvalues and associated eigenvectors.Generally in such a case derivatives in the Frchet sense do not exist, but only in the Gteaux sense.The formulas of the directional differential in the closed matrix form were derived.A numerical example is shown.