Some inequalities on generalized Schur complements
نویسندگان
چکیده
This paper presents some inequalities on generalized Schur complements. Let A be an n n (Hermitian) positive semide®nite matrix. Denote by A=a the generalized Schur complement of a principal submatrix indexed by a set a in A. Let A be the Moore± Penrose inverse of A and k A be the eigenvalue vector of A. The main results of this paper are: 1. k A a0P k A=a, where a0 is the complement of a in f1; 2; . . . ; ng. 2. k Ar=a6 k A=a for any real number r P 1: 3. C AC=a6C =a A a0 C=a for any matrix C of certain properties on partitioning. Ó 1999 Elsevier Science Inc. All rights reserved.
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