Article
Hua's Matrix Equality and Schur Complements
International Journal of Information & Systems Sciences
Document Type
Article
Publication Date
3-1-2008
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
Disciplines
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.
Citation Information
Chris Paige, George P. H. Styan, Bo-Ying Wang and Fuzhen Zhang. "Hua's Matrix Equality and Schur Complements" International Journal of Information & Systems Sciences Vol. 4 Iss. 1 (2008) p. 124 - 135 ISSN: 1708-296X Available at: http://works.bepress.com/fuzhen-zhang/55/