Journal of applied mathematics & informatics
- Volume 18 Issue 1_2
- /
- Pages.321-328
- /
- 2005
- /
- 2734-1194(pISSN)
- /
- 2234-8417(eISSN)
A MATRIX INEQUALITY ON SCHUR COMPLEMENTS
- YANG ZHONG-PENG (Department of Mathematics, Putian University) ;
- CAO CHONG-GUANG (School of Mathematical Science, Heilongjiang University) ;
- ZHANG XIAN (School of Mathematical Science, Heilongjiang University, School of Mechanical and Manufacturing Engineering)
- Published : 2005.03.01
Abstract
We investigate a matrix inequality on Schur complements defined by {1}-generalized inverses, and obtain simultaneously a necessary and sufficient condition under which the inequality turns into an equality. This extends two existing matrix inequalities on Schur complements defined respectively by inverses and Moore-Penrose generalized inverses (see Wang et al. [Lin. Alg. Appl., 302-303(1999)163-172] and Liu and Wang [Lin. Alg. Appl., 293(1999)233-241]). Moreover, the non-uniqueness of