Schur complements and determinant inequalities
Yan Zi-zong · Journal of Mathematical Inequalities · 2009
This paper is focused on the applications of Schur complements to determinant inequalities. It presents a monotonic characterization of Schur complements in the L wner partial ordering sense such that a new proof of the Hadamard-Fischer-Koteljanski inequality is obtained. Meanwhile, it presents matrix identities and determinant inequalities involving positive semidefinite matrices and extends the Hua Loo-keng determinant inequality by the technique of Schur complements.