The change of feedback invariants under one row perturbation
type: Item
instance of: scholarly article
title: The change of feedback invariants under one row perturbation
zbMATH Open document ID: 1117.15009
author: Marija Dodig
author: Marko Stošić
published in: Linear Algebra and its Applications
publication date: 2007-04-10T00:00:00Z
review text: The authors characterize possible feedback invariants of a rectangular matrix under small additive perturbations on one of its rows. Different authors have described the possible similarity invariants of a square matrix under small additive perturbations on one of its rows. Also, they have described the possible feedback invariants of matrices obtained by addition of a complex matrix with sufficiently small entries to an arbitrary rectangular complex matrix. This paper is a natural prolongation of those results. Let \(A \in \mathbb C^{n \times n}\), \(\mathbb C \in \mathbb C^{n \times m}\), \(b^T \in \mathbb C^{n \times 1}\), \(a \in \mathbb C^{1 \times n}\), \(c \in \mathbb C^{1 \times m}\) and \(x \in \mathbb C^{1 \times 1}\); and consider the following rectangular matrix \[ M= \left( \begin{matrix} A & b^T & C \\ a & x & c \end{matrix} \right). \] In this paper the authors study the feedback invariants of \(M\) under small perturbations on its row \([a, x, c]\). They obtain necessary and sufficient conditions in order to assure that in every neighbourhood of \(M\) there exists a matrix \[ M^{\prime}= \left( \begin{matrix} A & b^T & C \\ a' & x' & c' \end{matrix} \right) \] with a feedback invariants prescribed.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 5141637
zbMATH Keywords: Majorization
zbMATH Keywords: Row completions
zbMATH Keywords: Perturbations
reviewed by: Juan Ramón Torregrosa Sánchez
MaRDI profile type: Publication
full work available at URL: j.laa.2006.11.017
OpenAlex ID: W1994795194
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DOI: 10.1016/J.LAA.2006.11.017
description: scientific article; zbMATH DE number 5141637