Lipschitz properties of structure preserving matrix perturbations
type: Item
instance of: scholarly article
title: Lipschitz properties of structure preserving matrix perturbations
zbMATH Open document ID: 1298.15043
author: Leiba Rodman
published in: Linear Algebra and its Applications
publication date: 2012-08-27T00:00:00Z
review text: Perturbation theory of general matrices with the same Jordan structure has been developed by I. Gohberg, P. Lancaster and the author in connection with properties of their invariant subspace lattices. In this paper the author continues the study of matrices with the same Jordan structure, in particular their perturbation analysis. The main results concern the Lipschitz property of canonical transformation matrices (CTM's). This property says that the CTM's can be chosen so that the change in these matrices is of the same magnitude as that of a matrix perturbation, provided the latter preserves the matrix structure under investigation. The author proves that, under small perturbations preserving the Jordan structure, CTM's have the Lipschitz property. Analogous results are obtained for matrices with additional structure, such as Hamiltonian, skew-Hamiltonian and symplectic, including the real and complex cases.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 6072611
zbMATH Keywords: Jordan structure
zbMATH Keywords: matrix perturbations
zbMATH Keywords: Lipschitz property
zbMATH Keywords: Hamiltonian matrices
zbMATH Keywords: symplectic matrices
zbMATH Keywords: skew-Hamiltonian matrices
zbMATH Keywords: canonical transformation matrices
zbMATH Keywords: canonical forms
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: j.laa.2012.04.047
OpenAlex ID: W2030763461
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DOI: 10.1016/J.LAA.2012.04.047
description: scientific article; zbMATH DE number 6072611