Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices.