Some results on generalized Schur complement
Baowei Wu · Journal of Northwest University · 2004
AimTo study the quotient property and eigenvalues interlacing property of the generalized Schur complement.MethodsThe properties of positive semidefinite Hermitian matrices and Moore-Penrose inverse are used.ResultsA simple minimal representation,the quotient formula and several inequalities for the generalized Schur complement for positive semidefinite matrix are derived.ConclusionFor semidefinite Hermitian matrices, the quotient property and eigemalues interlacing result can be extended to the generalized Schur complement.But they do not hold for general Hermitian matrices.