New representations for weighted Drazin inverse of matrices
In this paper, the result are established in the following four ways: First, we present a general representation for the weighted Drazin inverse Ad,W of an arbitrary rectangular matrix A ∈ Mm,n involving Moore-Penrose inverse, which reduces to the well-known result if the matrix A is a square and W...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hikari
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/7871/1/New%20representations%20for%20weighted%20Drazin%20inverse%20of%20matrices.pdf |
| _version_ | 1796967414653517824 |
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| author | Al Zhour, Zeyad Abdel Aziz Kilicman, Adem Abu Hassan, Malik |
| author_facet | Al Zhour, Zeyad Abdel Aziz Kilicman, Adem Abu Hassan, Malik |
| author_sort | Al Zhour, Zeyad Abdel Aziz |
| collection | UPM |
| description | In this paper, the result are established in the following four ways: First, we present a general representation for the weighted Drazin inverse Ad,W of an arbitrary rectangular matrix A ∈ Mm,n involving Moore-Penrose inverse, which reduces to the well-known result if the
matrix A is a square and W = In . Second, we find represenations for the weighted Drazin inverse of the Tracy-Singh product A B of the two matrices A ∈ Mm,n and B ∈ Mp,q by using our approach. Third,the results are extended to the case of Tracy-Singh product of any finite
number of matrices.The result lead to equalities involving Kronecker product, Drazin inverse and group inverse, as a special case. Finally,We apply our result to present the solution of restricted singular matrix equations.
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| first_indexed | 2024-03-06T07:13:31Z |
| format | Article |
| id | upm.eprints-7871 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:13:31Z |
| publishDate | 2007 |
| publisher | Hikari |
| record_format | dspace |
| spelling | upm.eprints-78712015-12-08T07:53:57Z http://psasir.upm.edu.my/id/eprint/7871/ New representations for weighted Drazin inverse of matrices Al Zhour, Zeyad Abdel Aziz Kilicman, Adem Abu Hassan, Malik In this paper, the result are established in the following four ways: First, we present a general representation for the weighted Drazin inverse Ad,W of an arbitrary rectangular matrix A ∈ Mm,n involving Moore-Penrose inverse, which reduces to the well-known result if the matrix A is a square and W = In . Second, we find represenations for the weighted Drazin inverse of the Tracy-Singh product A B of the two matrices A ∈ Mm,n and B ∈ Mp,q by using our approach. Third,the results are extended to the case of Tracy-Singh product of any finite number of matrices.The result lead to equalities involving Kronecker product, Drazin inverse and group inverse, as a special case. Finally,We apply our result to present the solution of restricted singular matrix equations. Hikari 2007 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7871/1/New%20representations%20for%20weighted%20Drazin%20inverse%20of%20matrices.pdf Al Zhour, Zeyad Abdel Aziz and Kilicman, Adem and Abu Hassan, Malik (2007) New representations for weighted Drazin inverse of matrices. International Journal of Mathematical Analysis, 1 (15). pp. 697-708. ISSN 1312-8876; ESSN: 1314-7579 http://www.m-hikari.com/ijma/ijma-password-2007/ijma-password13-16-2007/alzhourIJMA13-16-2007.pdf |
| spellingShingle | Al Zhour, Zeyad Abdel Aziz Kilicman, Adem Abu Hassan, Malik New representations for weighted Drazin inverse of matrices |
| title | New representations for weighted Drazin inverse of matrices |
| title_full | New representations for weighted Drazin inverse of matrices |
| title_fullStr | New representations for weighted Drazin inverse of matrices |
| title_full_unstemmed | New representations for weighted Drazin inverse of matrices |
| title_short | New representations for weighted Drazin inverse of matrices |
| title_sort | new representations for weighted drazin inverse of matrices |
| url | http://psasir.upm.edu.my/id/eprint/7871/1/New%20representations%20for%20weighted%20Drazin%20inverse%20of%20matrices.pdf |
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