Publication:
Generic change of the partial multiplicities of regular matrix pencils under low-rank perturbations

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/31727
ISSN: 0895-4798
DOI: https://doi.org/10.1137/15M1022069
UXXI: AR/0000018402
Files
generic_SJMAA_2016_ps.pdf (396.34 KB)
Publication date
2016-01-01
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
We describe the generic change of the partial multiplicities at a given eigenvalue lambda(0) of a regular matrix pencil A(0) + lambda A(1) under perturbations with low normal rank. More precisely, if the pencil A(0) + lambda A(1) has exactly g nonzero partial multiplicities at lambda(0), then for most perturbations B-0 + lambda B-1 with normal rank r < g the perturbed pencil A(0) + B-0 + lambda(A(1) + B-1) has exactly g - r nonzero partial multiplicities at lambda(0), which coincide with those obtained after removing the largest r partial multiplicities of the original pencil A(0) + A(1) at lambda(0). Though partial results on this problem had been previously obtained in the literature, its complete solution remained open.
Description
Keywords
Regular matrix pencils, Weierstrass canonical form, Low-rank perturbations, Matrix spectral perturbation theory, Partial multiplicities, Geometric approach
Bibliographic citation
SIAM J. Matrix Anal. Appl., 37(3), 823–835
Collections
DM - AMCSS - Artículos de Revistas