Generic rank-two perturbations of structured regular matrix pencils
| dc.contributor.author | Batzke, Leonhard | |
| dc.date.accessioned | 2021-12-17T10:12:36Z | |
| dc.date.available | 2021-12-17T10:12:36Z | |
| dc.date.issued | 2014-07-28 | |
| dc.description.abstract | The spectral behavior of classes of structured regular matrix pencils is examined under certain structure-preserving rank-2 perturbations. For T-alternating, palindromic, and skew-symmetric matrix pencils we observe the following effects at each eigenvalue $\lambda$ under a generic, structure-preserving rank-2 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 $\lambda$. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15820 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14593 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | matrix pencil | en |
| dc.subject.other | alternating matrix pencil | en |
| dc.subject.other | palindromic matrix pencil | en |
| dc.subject.other | skew-symmetric matrix pencil | en |
| dc.subject.other | perturbation theory | en |
| dc.subject.other | rank two perturbation | en |
| dc.subject.other | generic perturbation | en |
| dc.title | Generic rank-two perturbations of structured regular matrix pencils | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2014, 09 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 15A18 Eigenvalues, singular values, and eigenvectors | en |
| tub.subject.msc2000 | 15A21 Canonical forms, reductions, classification | en |
| tub.subject.msc2000 | 15A22 Matrix pencils | en |
| tub.subject.msc2000 | 15B57 Hermitian, skew-Hermitian, and related matrices | en |
| tub.subject.msc2000 | 47A55 Perturbation theory | en |
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