Journal article
The normal defect of some classes of matrices
Linear algebra and its applications, v 438(8), pp 3530-3546
15 Apr 2013
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
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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Details
- Title
- The normal defect of some classes of matrices
- Creators
- Ryan D. Wasson - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- Linear algebra and its applications, v 438(8), pp 3530-3546
- Publisher
- Elsevier
- Number of pages
- 17
- Grant note
- DMS 0901628 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000316521500027
- Scopus ID
- 2-s2.0-84875442824
- Other Identifier
- 991019168516604721
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InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics
- Mathematics, Applied