International Journal of Information & Systems Sciences
Contractions, Contractive matrices, Generalized inverses, Hua matrix, Hua’s determinantal inequality, Hua’s matrix equality, Hua’s matrix inequality, Hua-Marcus inequalities, Inertia additivity, Matrix inequalities, Rank additivity, Schur complement, Sylvester’s law of inertia
The purpose of this paper is to revisit Hua's matrix equality (and inequality) through the Schur complement. We present Hua's original proof and two new proofs with some extensions of Hua's matrix equality and inequalities. The new proofs use a result concerning Shur complements and a generalization of Sylvester's law of inertia, each of which is useful in its own right.
Paige, Chris; Styan, George P. H.; Wang, Bo-Ying; and Zhang, Fuzhen, "Hua's Matrix Equality and Schur Complements" (2008). Mathematics Faculty Articles. 62.