Generalized Inverse of Generalized Schur Complement
Yang Zhong-peng · Journal of Mathematics and Technology · 2002
For four partitional matrix A=(A(α)A(α,α′)A(α′,α)A(α′))if A and A(α) are nonsingular, thenA -1(α′)=(A/α) -1,where A/α is Schur complement of A(α) in A Professor Wang BoYing point out that above equality d oes not generalize to the MoorePenrose inverse for positive semidefinite Herm itian Matrix. However, under some restiction, we prove that the relation between principal submatrix of generalized inverse and generalized Schur complement is close, therefore, classical result becomes special case.