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Keywords:
block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix
block circulant matrix; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; quaternionic matrix
Summary:
Let $ A_1, A_2,\cdots , A_n $ be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum $ \sum _{t=1}^{n} A_t$ can all be determined by the block circulant matrix generated by $ A_1, A_2, \cdots , A_n$. In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.
References:
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