The Moore-Penrose inverse of a partitioned nonnegative definite matrix

被引：6
|
作者：
Gross, J [1 ]
机构：
[1] Univ Dortmund, Dept Stat, D-44221 Dortmund, Germany
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 321卷 / 1-3期
关键词：
Banachiewicz inversion formula; generalized inverse; Lowner partial ordering; rank; Schur complement;
D O I：
10.1016/S0024-3795(99)00073-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Consider an arbitrary symmetric nonnegative definite matrix A and its Moore-Penrose inverse A(+), partitioned, respectively as A = ((E)(F') (F)(H)) and A(+) = ((Gt)(G2)(G2')(G4)). Explicit expressions for G(1), G(2) and G(4) in terms of E, F and H are given. Moreover, it is proved that the generalized Schur complement (A(+)/G(4)) = G(1) - G(2)G(4)(+)G'(2) is always below the Moore-Penrose inverse (A/H)(+) of the generalized Schur complement (A/H) = E - FH+F' with respect to the Lowner partial ordering. (C) 2000 Elsevier Science Inc. All rights reserved. AMS classification: 15A09.
引用
收藏
页码：113 / 121
页数：9
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