Author(s) :
Leonhard Batzke
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 092014
MSC 2000
 15A22 Matrix pencils

47A55 Perturbation theory
Abstract :
The spectral behavior of classes of structured regular matrix pencils is examined under certain structurepreserving rank2 perturbations.
For Talternating, palindromic, and skewsymmetric matrix pencils we observe the following effects at each eigenvalue $\lambda$ under a generic, structurepreserving rank2 perturbation:
1) The largest two Jordan blocks at $\lambda$ are destroyed.
2) If hereby the eigenvalue pairing imposed by the structure is violated, also the largest remaining Jordan block at $\lambda$ will grow in size by one.
3) If $\lambda$ is a single (double) eigenvalue of the perturbating pencil, one (two) new Jordan blocks of size one will be created at $\lambda$.
Keywords :
Matrix pencil, alternating matrix pencil, palindromic matrix pencil, skewsymmetric matrix pencil, perturbation theory, rank two perturbation, generic perturbation