Special rank-one perturbations
type: Item
instance of: scholarly article
title: Special rank-one perturbations
zbMATH Open document ID: 0855.15005
DOI: 10.1016/0024-3795(94)00135-9
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 1997-02-04T00:00:00Z
review text: The characteristic polynomial \(\Delta_\zeta\) is given for a rank-one perturbation \(\xi =A-cb^T\) in which \(A\) is square and \(f(A)c = 0\) for some polynomial \(f (\lambda)\). This type of perturbation is then used to obtain a slightly more general characterization of complete controllability for a single-input system, in terms of the \(\lambda\)-adjoint. Also, this type of perturbation is used to generate a large class of simple matrix examples (possibly integer) with prescribed characteristic and minimal polynomials.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 871119
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: rank-one perturbation
zbMATH Keywords: complete controllability
zbMATH Keywords: single-input system
zbMATH Keywords: minimal polynomials
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00135-9
OpenAlex ID: W2034595590
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description: scientific article; zbMATH DE number 871119