منابع مشابه
The reverse order law (ab) = b†(a†abb†)†a† in rings with involution
Several equivalent conditions for the reverse order law (ab) = b†(a†abb†)†a† in rings with involution are presented. Also, we investigate necessary and sufficient conditions for (ab) = b†a† to hold.
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 کاملThe Jordan forms of AB and BA
The relationship between the Jordan forms of the matrix products AB and BA for some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1. We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.
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: Linear Algebra and its Applications
سال: 1974
ISSN: 0024-3795
DOI: 10.1016/0024-3795(74)90023-8