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The normal defect of some classes of matrices
Journal article   Open access   Peer reviewed

The normal defect of some classes of matrices

Ryan D. Wasson and Hugo J. Woerdeman
Linear algebra and its applications, v 438(8), pp 3530-3546
15 Apr 2013
url
https://doi.org/10.1016/j.laa.2012.12.046View
Published, Version of Record (VoR)Open Access (Publisher-Specific) Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
An n x n matrix A has a normal defect of k if there exists an (n + k) x (n + k) normal matrix A(ext) with A as a leading principal sub-matrix and k minimal. In this paper we compute the normal defect of a special class of 4 x 4 matrices, namely matrices whose only nonzero entries lie on the superdiagonal, and we provide details for constructing minimal normal completion matrices Aext. We also prove a result for a related class of n x n matrices. Finally, we present an example of a 6 x 6 block diagonal matrix having the property that its normal defect is strictly less than the sum of the normal defects of each of its blocks, and we provide sufficient conditions for when the normal defect of a block diagonal matrix is equal to the sum of the normal defects of each of its blocks. (C) 2013 Elsevier Inc. All rights reserved.

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