The λ-Aluthge Transform of EP Matrices

In this work we present some relationships between an EP matrix T, its Aluthge transform Delta(T) or the lambda-Aluthge transform Delta(lambda)(T) and the Moore-Penrose inverse T-dagger. We prove that the lambda-Aluthge transform of T is also an EP matrix, and the same thing holds for Delta(lambda)(T-dagger)dagger and Delta(lambda)(T-dagger). Also, we explore the product Delta(lambda)(T)T, the connections between Delta(T) and T-dagger as well as the reverse order law for generalized inverses which are associated with Delta(lambda)(T). Finally, it is verified that the ranges of T and Delta(lambda)(T) are equal in the case of EP matrices.