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 Schur complements and a generalization of Sylvester’s law of inertia, each of which is useful in its own right.

in the civil procedure act, local inquiry is explained in a chapter separate from testimony, but for similarity of these two proofs, connection of them and criterion of separating them is disputable. in this article, we will study in one portion the role of witness and testimony conditions and in other portion, the role of number, sexuality, locality and ceremonies in separating of these proofs...