# The reverse order law for theW-weighted Drazin inverse of multiple matrices product

• Guorong Wang
• Zhaoliang Xu
Article

## Abstract

By using the rank methods of matrix, a necessary and sufficient condition is established for reverse order law
$$\begin{gathered} WA_{d,W} W = (W_n (A_n )_{d,W_n } W_n )(W_{n - 1} (A_{n - 1} )_{d,W_{n - 1} } W_{n - 1} ) \hfill \\ ... (W_1 (A_1 )_{d,W_1 } W_1 ) \hfill \\ \end{gathered}$$
to hold for the W-weighted Drazin inverses, whereA =A 1 A 2 … A n andW =W n W n-1W 1. This result is the extension of the result proposed by [Linear Algebra Appl., 348(2002)265-272] and the result proposed by [J. Math. Research and Exposition. 19(1999)355-358].

15A09

## Key words and phrases

Moore-Penrose inverse Drazin inverse weighted Drazin inverse index of a matrix reverse order law

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