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Main Title: Generic rank-one perturbations of structured regular matrix pencils
Author(s): Batzke, Leonhard
Type: Research Paper
Abstract: Classes of regular, structured matrix pencils are examined with respect to their spectral behavior under a certain type of structure-preserving rank-1 perturbations. The observed effects are as follows: On the one hand, generically the largest Jordan block at each eigenvalue gets destroyed or becomes size one under a rank-1 perturbation, depending on that eigenvalue occuring in the perturbating pencil or not. On the other hand, certain Jordan blocks of T-alternating matrix pencils occur in pairs, so that in some cases, the largest block cannot just be destroyed or shrinked to size one without violating the pairing. Thus, the largest remaining Jordan block will typically increase in size by one in these cases. Finally, these results are shown to carry over to the classes of palindromic and symmetric matrix pencils.
Subject(s): matrix pencil
alternating matrix pencil
palindromic matrix pencil
symmetric matrix pencil
perturbation theory
rank one perturbation
generic perturbation
Issue Date: 29-Jan-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
15A22 Matrix pencils
15B57 Hermitian, skew-Hermitian, and related matrices
47A55 Perturbation theory
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 03
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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