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%Al Zhour
%Dr. Zeyad","math_upm@yahoo.com","
\section{Matrix Results on Weighted Drazin Inverse and Some Applications} By {Zeyad Al Zhour and Adem Kilicman}.  

\medskip  \noindent In this paper, we present two general representations of the weighted Drazin inverse $A_{d,W}$ of an arbitrary rectangular matrix $A \in M_{m,n}$  related to Moore-Penrose Inverse (MPI) and Kronecker product of matrices. These generalizations extend earlier results on the Drazin inverse $A_{d}$, group inverse $A_{g}$ and usual inverse $A^{-1}$. %&#8315;©ö$.
 Furthermore, some necessary and sufficient conditions for Drazin and weighted Drazin inverses are given for
 the reverse order law $(AB)_{d}=B_{d}A_{d} $ and $(AB)_{d,Z}=B_{d,R}A_{d,W}$  to hold. Finally, we present the solution of the restricted singular matrix equations using our new approaches.
%Kronecker Product, Weighted Drazin Inverses, General algebraic structures, Index. Nilpotent matrix.","15A69","15A09",12:51:50","Tue Dec 25 2007","217.144.8.99"
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