Generic Change of the Partial Multiplicities of Regular Matrix Pencils under Low-Rank Perturbations
Fernando De Terán, Froilán M. Dopico · SIAM Journal on Matrix Analysis and Applications · 2016
We describe the generic change of the partial multiplicities at a given eigenvalue $\lambda_0$ of a regular matrix pencil $A_0+\lambda A_1$ under perturbations with low normal rank. More precisely, if the pencil $A_0+\lambda A_1$ has exactly $g$ nonzero partial multiplicities at $\lambda_0$, then for most perturbations $B_0+\lambda B_1$ with normal rank $r