一个2×2块矩阵的Moore-Penrose逆的显式公式

doi:10.13371/j.cnki.chin.q.j.m.2023.04.007

数学季刊 ›› 2023, Vol. 38 ›› Issue (4): 401-409.doi: 10.13371/j.cnki.chin.q.j.m.2023.04.007

一个2×2块矩阵的Moore-Penrose逆的显式公式

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

收稿日期:2022-05-10 出版日期:2023-12-30 发布日期:2023-12-30
通讯作者: YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics. E-mail:yuanyx 703@163.com
作者简介:ZENG Min (1999-), female, native of Jingzhou, Hubei, postgraduate student of Hubei Normal University, engages in computational mathematics; YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.

The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received:2022-05-10 Online:2023-12-30 Published:2023-12-30
Contact: YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics. E-mail:yuanyx 703@163.com
About author:ZENG Min (1999-), female, native of Jingzhou, Hubei, postgraduate student of Hubei Normal University, engages in computational mathematics; YUAN Yong-xin (1966-), male, native of Zhenjiang, Jiangsu, professor of Hubei Normal University, engages in computational mathematics.

摘要/Abstract

摘要： The representation for the Moore-Penrose inverse of the matrix
A B
C D
is derived by using the solvability theory of linear equations, where A∈C^m×n, B∈C^m×p, C∈C^q×nand D∈C^q×p, with which some special cases are discussed.

关键词: Block matrix, Moore-Penrose inverse, Linear equation

Abstract: The representation for the Moore-Penrose inverse of the matrix
A B
C D
is derived by using the solvability theory of linear equations, where A∈C^m×n, B∈C^m×p, C∈C^q×nand D∈C^q×p, with which some special cases are discussed.

Key words: Block matrix, Moore-Penrose inverse, Linear equation

中图分类号:

O241.6

曾敏, 袁永新. 一个2×2块矩阵的Moore-Penrose逆的显式公式[J]. 数学季刊, 2023, 38(4): 401-409.

ZENG Min, YUAN Yong-xin. The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 401-409.

[1]	杜法鹏. 2×2分块矩阵群逆的表示[J]. 数学季刊, 2016, 31(4): 412-421.
[2]	杜法鹏, 薛以锋. a-xy*的Moore-Penrose逆的表示的统一方法[J]. 数学季刊, 2014, 29(3): 465-474.
[3]	杜法鹏, 薛以锋. 闭算子Moore-Penrose逆的逆序律[J]. 数学季刊, 2013, 28(1): 139-146.
[4]	袁功林, 韦增欣, 鲁习文. 一个求解非线性对称方程组的非单调信赖域方法[J]. 数学季刊, 2009, 24(4): 574-584.
[5]	武跃祥, 王拉娣 . 极大单调映象的满射定理及其应用[J]. 数学季刊, 2008, 23(4): 615-620.
[6]	唐荣荣. 一类强非线性奇摄动边值问题[J]. 数学季刊, 2003, 18(2): 117-120.

一个2×2块矩阵的Moore-Penrose逆的显式公式

The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix

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