Some inequalities for eigenvalues of Schur complements of Hermitian matrices

Authors:
Jianzhou Liu;Yunqing Huang;Anping Liao
Affiliations:
Department of Mathematics, Xiangtan University, Xiangtan, Hunan, PR China;Department of Mathematics, Xiangtan University, Xiangtan, Hunan, PR China;College of Mathematics and Econometrices, Hunan University, Changsha, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

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 B A B in terms of the eigenvalues of the Schur complements of BB and A.