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Main Title: Low rank perturbation of regular matrix pencils with symmetry structures
Author(s): De Terán, Fernando
Mehl, Christian
Mehrmann, Volker
Type: Research Paper
Abstract: The generic change of the Weierstraß Canonical Form of regular complex structured matrix pencils under generic structure-preserving additive low-rank perturbations is studied. Several different symmetry structures are considered and it is shown that for most of the structures, the generic change in the eigenvalues is analogous to the case of generic perturbations that ignore the structure. However, for some odd/even and palindromic structures, there is a di erent behavior for the eigenvalues 0 and 1, respectively +1 and -1. The differences arise in those cases where the parity of the partial multiplicities in the perturbed pencil provided by the generic behavior in the general structure-ignoring case is not in accordance with the restrictions imposed by the structure. The new results extend results for the rank-1 and rank- 2 cases that were obtained in [3, 5] for the case of special structure-preserving perturbations. As the main tool, we use decompositions of matrix pencils with symmetry structure into sums of rank-one pencils, as those allow a parametrization of the set of matrix pencils with a given symmetry structure and a given rank.
Subject(s): even matrix pencil
palindromic matrix pencil
Hermitian matrix pencil
symmetric matrix pencil
skew-symmetric matrix pencil
perturbation analysis
generic perturbation
low-rank perturbation
additive decomposition of structured pencils
Weierstraß canonical form
Issue Date: 1-Feb-2019
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A22 Matrix pencils
15A18 Eigenvalues, singular values, and eigenvectors
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2019, 04
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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