Generic rank-two perturbations of structured regular matrix pencils
Leonhard Batzke · Operators and Matrices · 2016
The generic spectral behavior of classes of structured regular matrix pencils is examined under structure-preserving rank-2 perturbations, i.e., perturbations of normal rank two. For T -alternating, palindromic, and skew-symmetric matrix pencils we observe the following effects at each eigenvalue under a generic, structure-preserving rank-2 perturbation: 1) The largest two Jordan blocks at are destroyed. 2) If hereby the eigenvalue pairing imposed by the structure is violated, also the largest remaining Jordan block at will grow in size by one. 3) If is a single (double) eigenvalue of the perturbating pencil, one (two) new Jordan blocks of size one will be created at .