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Main Title: Sign characteristics of regular Hermitian matrix pencils under generic rank-1 and rank-2 perturbations
Author(s): Batzke, Leonhard
Type: Research Paper
Abstract: The spectral behavior of regular Hermitian matrix pencils is examined under certain structure-preserving rank-1 and rank-2 perturbations. Since Hermitian pencils have signs attached to real (and infinite) blocks in canonical form, it is not only the Jordan structure but also this so-called sign characteristic that needs to be examined under perturbation. The observed effects are as follows: Under a rank-1 or rank-2 perturbation, generically the largest one or two, respectively, Jordan blocks at each eigenvalue λ are destroyed, and if λ is an eigenvalue of the perturbation, also one new block of size one is created at λ. If λ is real (or infinite), additionally all signs at λ but one or two, respectively, that correspond to the destroyed blocks, are preserved under perturbation. Also, if the potential new block of size one is real, its sign is in most cases prescribed to be the sign that is attached to the eigenvalue λ in the perturbation.
Subject(s): matrix pencil
Hermitian matrix pencil
sign characteristic
rank one perturbation
rank two perturbation
generic perturbation
Issue Date: 24-Nov-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A22 Matrix pencils
47A55 Perturbation theory
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 36
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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