On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications

Tian and Styan have shown many rank equalities for the sum of two and three idempotent matrices and pointed out that rank equalities for the sum P (1) + ⋯+P (k) with P (1),…, P (k) be idempotent (k > 3) are still open. In this paper, by using block Gaussian elimination, we obtained rank equalitie...

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Detalles Bibliográficos
Autores principales: Chen, Mei-xiang, Chen, Qing-hua, Li, Qiao-xin, Yang, Zhong-peng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4121197/
https://www.ncbi.nlm.nih.gov/pubmed/25121133
http://dx.doi.org/10.1155/2014/702413
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author Chen, Mei-xiang
Chen, Qing-hua
Li, Qiao-xin
Yang, Zhong-peng
author_facet Chen, Mei-xiang
Chen, Qing-hua
Li, Qiao-xin
Yang, Zhong-peng
author_sort Chen, Mei-xiang
collection PubMed
description Tian and Styan have shown many rank equalities for the sum of two and three idempotent matrices and pointed out that rank equalities for the sum P (1) + ⋯+P (k) with P (1),…, P (k) be idempotent (k > 3) are still open. In this paper, by using block Gaussian elimination, we obtained rank equalities for the sum of finitely many idempotent matrices and then solved the open problem mentioned above. Extensions to scalar-potent matrices and some related matrices are also included.
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spelling pubmed-41211972014-08-12 On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications Chen, Mei-xiang Chen, Qing-hua Li, Qiao-xin Yang, Zhong-peng ScientificWorldJournal Research Article Tian and Styan have shown many rank equalities for the sum of two and three idempotent matrices and pointed out that rank equalities for the sum P (1) + ⋯+P (k) with P (1),…, P (k) be idempotent (k > 3) are still open. In this paper, by using block Gaussian elimination, we obtained rank equalities for the sum of finitely many idempotent matrices and then solved the open problem mentioned above. Extensions to scalar-potent matrices and some related matrices are also included. Hindawi Publishing Corporation 2014 2014-07-10 /pmc/articles/PMC4121197/ /pubmed/25121133 http://dx.doi.org/10.1155/2014/702413 Text en Copyright © 2014 Mei-xiang Chen et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Chen, Mei-xiang
Chen, Qing-hua
Li, Qiao-xin
Yang, Zhong-peng
On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
title On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
title_full On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
title_fullStr On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
title_full_unstemmed On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
title_short On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
title_sort on the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4121197/
https://www.ncbi.nlm.nih.gov/pubmed/25121133
http://dx.doi.org/10.1155/2014/702413
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