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Main Title: Generic rank-two perturbations of structured regular matrix pencils
Author(s): Batzke, Leonhard
Type: Research Paper
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 $\lambda$.
Subject(s): matrix pencil
alternating matrix pencil
palindromic matrix pencil
skew-symmetric matrix pencil
perturbation theory
rank two perturbation
generic perturbation
Issue Date: 28-Jul-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, 09
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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