Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

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

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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 $\{1\}$-generalized inverses yields the complicatedness of the extension.

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