On the Block Independence in Generalized Moore-Penrose Inverse and Group Inverse of Block Matrix over Rings

摘要

In this paper, the block independence in generalized Moore-Penrose inverse and group inverse of block matrices over rings are discussed. We give the definition of block independence in generalized Moore-Penrose inverse of 2×2 block matrix over a generalized weak finite ring, and derive necessary and sufficient conditions for block independence in generalized Moore-Penrose inverse of 2×2 block matrix. An analogous set of conditions for block independence in group inverse of 2×2 block matrix over rings is also obtained.