Further results on the reverse-order law
نویسندگان
چکیده
منابع مشابه
Further Results on the Reverse Order Law for Generalized Inverses
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.
متن کاملFurther results on the reverse order law for the Moore-Penrose inverse in rings with involution
We present some equivalent conditions of the reverse order law for the Moore–Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore-Penrose inverse in C∗-algebras.
متن کاملFurther results on the reverse order law for the group inverse in rings
In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both involved elements are EP.
متن کاملThe 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...
متن کاملSome results on the reverse order law in rings with involution
We investigate some necessary and sufficient conditions for the hybrid reverse order law (ab) = b†a† in rings with involution. Assuming that a and b are Moore-Penrose invertible, we present equivalent condition for the product ab to be EP element.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1979
ISSN: 0024-3795
DOI: 10.1016/0024-3795(79)90027-2