华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 4: 38 - 43

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.04.005

数学

2x2分块矩阵中Schur补的广义逆表示 (英)

  • 郭美华 ,
  • 刘丁酉
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  • 武汉大学 数学与统计学院, 武汉 430000

收稿日期: 2015-06-04

  网络出版日期: 2016-09-29

基金资助

国家自然科学基金(11371284)

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Expressions on generalized inverses of the Schur complement of a 2×2 block matrix

  • GUO Mei-hua ,
  • LIU Ding-you
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  • School of Mathematics and Statistics, Wuhan UniversityWuhan 430000, China

Received date: 2015-06-04

  Online published: 2016-09-29

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摘要

本文主要研究了不同条件下同一个2x2 分块矩阵 M=\left(
                              \begin{array}{cc}
                                A & B \\
                                C & D \\
                              \end{array}
                            \right)
中 Schur 补的广义逆 S=A-BD^{-}C 不同的表示形式, 特别地, 当 M 是一个半正定 Hermite 阵时, 可以得到关于 Schur 补的广义逆的一些新形式, 并由此得到一些推论.

关键词： 2x2分块矩阵; 广义逆; Schur 补

本文引用格式

郭美华, 刘丁酉. 2x2分块矩阵中Schur补的广义逆表示 (英)[J]. 华东师范大学学报（自然科学版）, 2016, 2016(4): 38-43. DOI: 10.3969/j.issn.1000-5641.2016.04.005

Abstract

This article investigates various expressions for the generalized inverses of the Schur complement S = A − BD−C of a 2 × 2 block matrix M =
A B
C D
!
under different conditions. Moreover, we give some new results for the generalized inverses of the Schur complement when M is positive semidefinite. Besides, some conclusions are obtained directly from our results.

Key words： 2 ×; 2 block matrix; generalized inverse; Schur complement

参考文献

[ 1 ] RAO C R, MITRA S K. Generalized inverse of a matrix and its applications [C]//Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. 1972, 1: 601-620.
[ 2 ] 郭美华, 刘丁酉. 分块 2 次幂零矩阵的广义 Schur 补 [J]. 武汉大学学报 (理学版), 2015, 61(6): 563-567.
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[ 9 ] PRINGLE R M, RAYNER A A. Expressions for generalized inverses of a bordered matrix with application to the theory of constrained linear models [J]. SIAM Review, 1970, 12(1): 107-115.

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