A B On the Block Independence in g-Inverse of a Matrix (A B C O)

Abstract:

      In this paper, we -proved a interesting fact that the rank additivity condition rank (A B C 0) = rank (A C) + rank (B 0) = rank(A,B)+ rank(C, 0)is a necessary and sufficient condition for block independence in g-inverse of (A B C 0),and moreover for that the Moore-Penrose inverse of (A B C 0) is(?) where Q=[(I- BB⁺)A(I-C⁺C)]⁺.