Eigenvalues of parametric rank-one perturbations of matrix pencils

Abstract

We study the behavior of eigenvalues of regular matrix pencils under rank-one perturbations which depend on a scalar parameter. In particular, the change of the algebraic multiplicities, the change of the eigenvalues for small parameter variations, as well as the asymptotic eigenvalue behavior as the parameter tends to infinity, is described. Besides that, an interlacing result for rank-one perturbations of matrix pencils is obtained. Finally, we show how to use these results in the redesign of electrical circuits, like for the low pass filter or for a two-stage CMOS operational amplifier.