Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14593
 Main Title: Generic rank-two perturbations of structured regular matrix pencils Author(s): Batzke, Leonhard Type: Research Paper URI: https://depositonce.tu-berlin.de/handle/11303/15820http://dx.doi.org/10.14279/depositonce-14593 License: http://rightsstatements.org/vocab/InC/1.0/ 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 pencilalternating matrix pencilpalindromic matrix pencilskew-symmetric matrix pencilperturbation theoryrank two perturbationgeneric 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 eigenvectors15A21 Canonical forms, reductions, classification15A22 Matrix pencils15B57 Hermitian, skew-Hermitian, and related matrices47A55 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