Perturbation of the Eigenvalues of Quadratic Matrix Polynomials
Heinz Langer, Branko Najman, Krešimir Veselić · SIAM Journal on Matrix Analysis and Applications · 1992
Perturbation properties of a quadratic matrix pencil containing a “small” parameter are considered. Main results concern the splitting properties of multiple eigenvalues and the corresponding Puiseux expansions. For hermitian pencils it is proved that the Puiseux expansion generates groups of eigenvalues ordered according to the partial algebraic multiplicities of the unperturbed eigenvalue.