Further results on partial ordering and the generalized inverses
Long Wang, Jianlong Chen · Linear and Multilinear Algebra · 2015
In this paper, some results relating left-starleft star ordering and core partial ordering are obtained under certain conditions in rings with involution. Some inheritance properties of the left star partial order are considered. The conditions for to be MP invertible (resp., group invertible) are given whenever is MP-invertible (resp., EP) satisfying . Moreover, necessary and sufficient conditions for the invertibility and the Moore-PenroseMoore–Penrose invertibility of the linear combination are investigated.