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 P1+⋯+Pk with P1,…,Pk be idempotent (k>3) are still open. In this paper, by using block Gaussian elimination, we obtained rank equalities for the sum of...
| Published in: | The Scientific World Journal |
|---|---|
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Online Access: | http://dx.doi.org/10.1155/2014/702413 |
| _version_ | 1849439032257282048 |
|---|---|
| author | Mei-xiang Chen Qing-hua Chen Qiao-xin Li Zhong-peng Yang |
| author_facet | Mei-xiang Chen Qing-hua Chen Qiao-xin Li Zhong-peng Yang |
| author_sort | Mei-xiang Chen |
| collection | DOAJ |
| container_title | The Scientific World Journal |
| 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 P1+⋯+Pk with P1,…,Pk 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. |
| format | Article |
| id | doaj-art-4ba679aba78b414fbbd85cf0c199b04d |
| institution | Directory of Open Access Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| spelling | doaj-art-4ba679aba78b414fbbd85cf0c199b04d2025-08-20T03:34:18ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/702413702413On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its ApplicationsMei-xiang Chen0Qing-hua Chen1Qiao-xin Li2Zhong-peng Yang3School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, ChinaSchool of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, ChinaInstitute of Applied Physics and Computational Mathematics, Beijing 100094, ChinaSchool of Mathematics, Putian University, Putian, Fujian 351100, ChinaTian 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 P1+⋯+Pk with P1,…,Pk 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.http://dx.doi.org/10.1155/2014/702413 |
| spellingShingle | Mei-xiang Chen Qing-hua Chen Qiao-xin Li Zhong-peng Yang 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 |
| url | http://dx.doi.org/10.1155/2014/702413 |
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