Further Results on the Reverse Order Law for Generalized Inverses
نویسنده
چکیده
The reverse order rule (AB)† = B†A† for the Moore-Penrose inverse is established in several equivalent forms. Results related to other generalized inverses are also proved.
منابع مشابه
The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...
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ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 29 شماره
صفحات -
تاریخ انتشار 2007