广东工业大学学报 ›› 2012, Vol. 29 ›› Issue (2): 72-75.doi: 10.3969/j.issn.1007-7162.2012.02.014

• 综合研究 • 上一篇    下一篇

列分块矩阵的MoorePenrose逆

  

  1. 1．广东工业大学 应用数学学院, 广东 广州 510520；2．浙江财经学院 数学与统计学院，浙江 杭州 310018
  • 出版日期:2012-06-25 发布日期:2012-06-25
  • 作者简介:邱红兵（1974-），男，副教授，主要研究方向为线性模型、矩阵分析.
  • 基金资助:

    国家自然科学基金资助项目(11171058)；浙江省自然科学基金资助项目(Y6110615)；国家社会科学基金资助项目(11CTJ008)

The Moore-Penrose Inverse of Column Partitioned Matrix

  1. 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
    2.Mathematics and Statistics School, Zhejiang University of Finance and Economics, Hangzhou 310018, China
  • Online:2012-06-25 Published:2012-06-25

HTML

PDF (PC)

2992

摘要： 利用矩阵分块，给出了求一般矩阵MoorePenrose逆的一种新方法，且新方法只需利用矩阵的初等变换即可实现.

关键词: 列分块矩阵；广义逆；转置；MoorePenrose逆；初等变换

Abstract: A new method of solving the MoorPenrose inverse of a matrix with partitioned matrix is given, and the method can be realized only with the elementary transformation of matrix.

Key words: column partitioned matrix; generalized inverse; transposition; MoorePenrose inverse; elementary transformation

［1］ Cline R E.Representations for the generalized inverse of a partitioned matrix［J］. J Soc Indust Apple Math, 1964(12): 588-600.

［2］ Mihályffy L. An alternative representation of the generalized inverse of partitioned matrices［J］. Linear Algebra and its Applications, 1971, 4: 95-100.

［3］ Jerzy K. Baksalary，Oskar Maria Baksalary.Particular formulae for the MoorePenrose inverse of a columnwise partitioned matrix［J］. Linear Algebra and its Applications, 2007,421: 16-23.

［4］ Chen Yong-lin，Zhou Bingjun.On ginverses and the nonsingularity of a bordered matrix BC0［J］. Linear Algebra and its Applications, 1990,133: 133
［5］ Miao JianMing.General Expressions for the MoorePenrose Inverse of a 2×2 Block Matrix［J］. Linear Algebra and its Applications, 1991,15: 1-15.

［6］ 王松桂,杨振海．广义逆矩阵及其应用［M］．北京：北京工业大学出版社,1996.

［7］ 陈永林.广义逆矩阵的理论和方法［M］．南京：南京师范大学出版社，2005．

［8］ Yongge tain.Eight expressions for generalized inverses of a bordered matrix［J］. Linear and Multilinear Algebra, 2009(1): 1-18.

［9］ 倪国熙．常用的矩阵理论和方法［M］．上海：上海科学技术出版社，1984.
No related articles found!
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发