Low rank perturbations of quaternion matrices
| dc.contributor.author | Mehl, Christian | |
| dc.contributor.author | Ran, André | |
| dc.date.accessioned | 2021-12-17T10:14:51Z | |
| dc.date.available | 2021-12-17T10:14:51Z | |
| dc.date.issued | 2017-10-02 | |
| dc.description.abstract | Low rank perturbations of right eigenvalues of quaternion matrices are considered. For real and complex matrices it is well known that under a generic rank-k perturbation the k largest Jordan blocks of a given eigenvalue will disappear while additional smaller Jordan blocks will remain. In this paper, it is shown that the same is true for real eigenvalues of quaternion matrices, but for complex nonreal eigenvalues the situation is different: not only the largest k, but the largest 2k Jordan blocks of a given eigenvalue will disappear under generic quaternion perturbations of rank k. Special emphasis is also given to Hermitian and skew-Hermitian quaternion matrices and generic low rank perturbations that are structure-preserving. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15887 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14660 | |
| 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 | quaternions | en |
| dc.subject.other | eigenvalues | en |
| dc.subject.other | perturbation theory | en |
| dc.subject.other | low rank perturbations | en |
| dc.title | Low rank perturbations of quaternion matrices | 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 | 2017, 10 | en |
| tub.series.name | Preprint-Reihe des Instituts fĂ¼r Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 15A33 Matrices over special rings | en |
| tub.subject.msc2000 | 15A18 Eigenvalues, singular values, and eigenvectors | en |
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