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

Yongge Tian

Address. Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, CANADA K7L 3N6


Abstract. 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.

AMSclassification. 15A09, 15A23

Keywords. Block circulant matrix, Moore-Penrose inverse, Drazin inverse, weighted Moore-Penrose inverse,
                   quaternionic matrix