The Generalized Inverse A(2)T, Sof a Matrix Over an Associative Ring
2007 ◽
Vol 83
(3)
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pp. 423-438
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Keyword(s):
AbstractIn this paper we establish the definition of the generalized inverse A(2)T, Swhich is a {2} inverse of a matrixAwith prescribed imageTand kernelsover an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverseand some explicit expressions forof a matrix A over an associative ring, which reduce to the group inverse or {1} inverses. In addition, we show that for an arbitrary matrixAover an associative ring, the Drazin inverse Ad, the group inverse Agand the Moore-Penrose inverse. if they exist, are all the generalized inverse A(2)T, S.
2016 ◽
Vol 2016
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pp. 1-14
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2011 ◽
Vol 2011
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pp. 1-19
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2006 ◽
Vol 05
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pp. 537-548
1975 ◽
Vol 18
(1)
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pp. 7-17
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