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Some equalities for generalized inverses of matrix sums and block circulant matrices

Yong Ge Tian — 2001

Archivum Mathematicum

Let A 1 , A 2 , , 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 t = 1 n A t can all be determined by the block circulant matrix generated by A 1 , A 2 , , A n . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.

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