Some inequalities on generalized Schur complements

✍ Scribed by Bo-Ying Wang; Xiuping Zhang; Fuzhen Zhang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 92 KB
• Volume: 302-303
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00071-3

✦ Synopsis

This paper presents some inequalities on generalized Schur complements. Let A be an n  n (Hermitian) positive semide®nite matrix. Denote by eaa the generalized Schur complement of a principal submatrix indexed by a set a in A. Let e be the Moore± Penrose inverse of A and ke be the eigenvalue vector of A. The main results of this paper are: 1. ke a H P keaa , where a H is the complement of a in f1Y 2Y F F F Y ng. 2. ke r aa T k r eaa for any real number r P 1X 3. g à egaa T g à aa ea H gaa for any matrix C of certain properties on partitioning.