Based on the A(1,2)T,S inverse and the weak Core inverse,we propose the concept of generalized weak Core inverse.We study its characterization,representation and properties.We also give a variant of the successive matrix squaring computational iterative scheme for calculating the generalized weak Core inverse.Moreover,we study the Cramer's rule of the solution of the matrix equation Ax=B.Finally,we give the perturbations of the generalized weak Core inverse.
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