Some inequalities for eigenvalues of Schur complements of Hermitian matrices

In this paper, using a minimum principle for Schur complements of positive semidefinite Hermitian matrices and some estimates of the eigenvalues and the singular values, we obtain some inequalities for the eigenvalues of the Schur complement of the matrix product BAB*BAB* in terms of the eigenvalues of the Schur complements of BB*BB* and A.