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New representations for weighted Drazin inverse of matrices


Citation

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

Abstract

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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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Publisher: Hikari
Keywords: Tracy-Singh products; Weighted Drazin inverses; General algebraic structures; Index. Nilpotent matrix
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 25 May 2015 07:40
Last Modified: 08 Dec 2015 07:53
URI: http://psasir.upm.edu.my/id/eprint/7871
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