The reverse-order law $(AB)^{\dag}=B^{\dag}(A^{\dag}ABB^{\dag})^{\dag}A^{\dag}$ and its equivalent equalities
نویسندگان
چکیده
منابع مشابه
A new equivalent condition of the reverse order law for G-inverses of multiple matrix products
In 1999, Wei [M.Wei, Reverse order laws for generalized inverse of multiple matrix products, Linear Algebra Appl., 293 (1999), pp. 273-288] studied reverse order laws for generalized inverses of multiple matrix products and derived some necessary and sufficient conditions for An{1}An−1{1} · · ·A1{1} ⊆ (A1A2 · · ·An){1} by using P-SVD (Product Singular Value Decomposition). In this paper, using ...
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 کاملReverse order law in C∗-algebras
We study equivalent conditions for the reverse order law (a1a2 . . . an)† = an(a † 1a1a2 . . . ana † n) †a1 in C ∗-algebras. As corollaries, we obtain some recent and special results.
متن کاملEla a New Equivalent Condition of the Reverse Order Law for G-inverses of Multiple Matrix Products∗
In 1999, Wei [M.Wei, Reverse order laws for generalized inverse of multiple matrix products, Linear Algebra Appl., 293 (1999), pp. 273-288] studied reverse order laws for generalized inverses of multiple matrix products and derived some necessary and sufficient conditions for An{1}An−1{1} · · ·A1{1} ⊆ (A1A2 · · ·An){1} by using P-SVD (Product Singular Value Decomposition). In this paper, using ...
متن کاملFurther 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.
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 2005
ISSN: 2156-2261
DOI: 10.1215/kjm/1250281660