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.
@article{107808,
author = {Yong Ge Tian},
title = {Some equalities for generalized inverses of matrix sums and block circulant matrices},
journal = {Archivum Mathematicum},
volume = {037},
year = {2001},
pages = {301-306},
zbl = {1090.15005},
mrnumber = {1879453},
language = {en},
url = {http://dml.mathdoc.fr/item/107808}
}
Tian, Yong Ge. Some equalities for generalized inverses of matrix sums and block circulant matrices. Archivum Mathematicum, Tome 037 (2001) pp. 301-306. http://gdmltest.u-ga.fr/item/107808/
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