Mathematics Faculty Articles

Document Type

Article

Publication Date

3-1-2008

Publication Title

International Journal of Information & Systems Sciences

Keywords

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

ISSN

1708-296X

Volume

4

Issue/No.

1

First Page

124

Last Page

135

Abstract

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.

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