Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices
We give a formula of (P+Q)D under the conditions P2Q+QPQ=0, P3Q=0, and PQPQ=0. Then, we apply it to give some expressions for the Drazin inverse of block matrix M=(ABCD) (A and D are square matrices) under some conditions, generalizing some recent results in the literature. Finally, numerical examp...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/804313 |
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| author | Abdul Shakoor Hu Yang Ilyas Ali |
| author_facet | Abdul Shakoor Hu Yang Ilyas Ali |
| author_sort | Abdul Shakoor |
| collection | DOAJ |
| description | We give a formula of (P+Q)D under the conditions P2Q+QPQ=0, P3Q=0, and PQPQ=0. Then, we apply it to give some expressions for the Drazin inverse of block matrix M=(ABCD) (A and D are square matrices) under some conditions, generalizing some recent results in the literature. Finally, numerical examples are given to illustrate our results. |
| format | Article |
| id | doaj-art-adc97383ef654d909b53f8c862d7b20d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-adc97383ef654d909b53f8c862d7b20d2025-02-03T01:30:34ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/804313804313Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block MatricesAbdul Shakoor0Hu Yang1Ilyas Ali2College of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaCollege of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaCollege of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaWe give a formula of (P+Q)D under the conditions P2Q+QPQ=0, P3Q=0, and PQPQ=0. Then, we apply it to give some expressions for the Drazin inverse of block matrix M=(ABCD) (A and D are square matrices) under some conditions, generalizing some recent results in the literature. Finally, numerical examples are given to illustrate our results.http://dx.doi.org/10.1155/2013/804313 |
| spellingShingle | Abdul Shakoor Hu Yang Ilyas Ali Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices Journal of Applied Mathematics |
| title | Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices |
| title_full | Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices |
| title_fullStr | Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices |
| title_full_unstemmed | Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices |
| title_short | Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices |
| title_sort | some results for the drazin inverses of the sum of two matrices and some block matrices |
| url | http://dx.doi.org/10.1155/2013/804313 |
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