分块矩阵广义逆的反问题

The Inverse Problem for the Generalized Inverses of Partitioned Matrix

设M =AXX′C 是实对称矩阵 ,X是列满秩矩阵 ,G =BYY′D 是实对称矩阵 .当G是M的g -逆、反射g -逆、Moore -Penrose逆时 ,本文给出了B为A的g -逆、反射g -逆、Moore -Pen rose逆的条件及A的g -逆、反射g-逆、Moore -Penrose逆的表达式 .

Let M=is real symmetric matrix,X is of full column rank,and the real symmetric matrix G=is the generalized inverses of M.In this paper,we give the conditions that B is the g-inverse,reflexive inverse and Moore-Penrose inverse of A,and obtain formulae for the corresponding generalized inverses of A.