The λ-Aluthge transform of EP matrices
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In this work we present some relationships between an EP matrix T, its Aluthge transform ?(T) or the ?-Aluthge transform ??(T) and the Moore-Penrose inverse T+. We prove that the ?-Aluthge transform of T is also an EP matrix, and the same thing holds for ??(T)+ and ??(T+). Also, we explore the product ??(T)T, the connections between ?(T) and T+ as well as the reverse order law for generalized inverses which are associated with ??(T). Finally, it is verified that the ranges of T and ??(T) are equal in the case of EP matrices.
1998 ◽
Vol 277
(1-3)
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pp. 299-311
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2015 ◽
Vol 64
(7)
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pp. 1266-1282
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2002 ◽
Vol 125
(2-3)
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pp. 221-229
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2008 ◽
Vol 29
(4)
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pp. 1242-1246
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2011 ◽
Vol 36
(3)
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pp. 475-486
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