On group inverses and the sharp order
نویسندگان
چکیده
منابع مشابه
Group Inverses and Drazin Inverses over Banach Algebras
For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...
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...
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Nonnegative rectangular matrices having nonnegative Unweighted group inverses are characterized. Our techniques suggest an interesting approach to extend the earlier known results on X-monotone square matrices to rectangular ones. We also answer a question of characterizing nonnegative matrices having a nonnegative solution Y where (1) A = AXA, (2) X = XAX, (3) (AX) is O-symmetric, (4) ( XA) is...
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.
متن کاملA note on the order graph of a group
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1987
ISSN: 0024-3795
DOI: 10.1016/0024-3795(87)90248-5