The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices

The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequa...

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Detalles Bibliográficos
Autores principales: Wang, Dafei, Zhang, Xumei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5519689/
https://www.ncbi.nlm.nih.gov/pubmed/28794607
http://dx.doi.org/10.1186/s13660-017-1446-4
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author Wang, Dafei
Zhang, Xumei
author_facet Wang, Dafei
Zhang, Xumei
author_sort Wang, Dafei
collection PubMed
description The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced. Furthermore, based on the estimation for the rank, some sufficient conditions for nonsingular matrices are obtained.
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spelling pubmed-55196892017-08-07 The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices Wang, Dafei Zhang, Xumei J Inequal Appl Research The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced. Furthermore, based on the estimation for the rank, some sufficient conditions for nonsingular matrices are obtained. Springer International Publishing 2017-07-20 2017 /pmc/articles/PMC5519689/ /pubmed/28794607 http://dx.doi.org/10.1186/s13660-017-1446-4 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Wang, Dafei
Zhang, Xumei
The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
title The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
title_full The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
title_fullStr The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
title_full_unstemmed The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
title_short The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
title_sort lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5519689/
https://www.ncbi.nlm.nih.gov/pubmed/28794607
http://dx.doi.org/10.1186/s13660-017-1446-4
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