华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (5): 33-37,4.

• 应用数学与基础数学 • 上一篇    下一篇

A-XY*的Moore-Penrose逆的表示

杜法鹏1,2, 薛以锋1   

  1. 1. 华东师范大学 数学系, 上海 200241; 2. 徐州工程学院 数理学院, 江苏 徐州 221008
  • 收稿日期:2010-01-01 修回日期:2010-05-01 出版日期:2010-09-25 发布日期:2010-09-25
  • 通讯作者: 杜法鹏

Expression of the Moore-Penrose inverse of A-XY*

DU Fa-peng1,2, XUE Yi-feng1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. College of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou Jiangsu 221008, China
  • Received:2010-01-01 Revised:2010-05-01 Online:2010-09-25 Published:2010-09-25
  • Contact: DU Fa-peng

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摘要： 在Hilbert空间上有界线性算子的条件下, 进一步推广了Shermen-Morrison-Woodbury(SMW)公式的Moor-Penrose逆的表示. 这个公式可以用来计算A^+的某些扰动和某些算子矩阵的Moore--Penrose 逆.

关键词: Hilbert空间, Moore-Penrose逆, 幂等算子, Hilbert空间, Moore-Penrose逆, 幂等算子

Abstract: By using theory of bounded linear operators on Hilbert spaces, the Shermen-Morrison-Woodbury (SMW) formula's Moore-Penrose inverse was presented. The formula obtained can be used to compute certain perturbation of A^+ and the Moore--Penrose inverses of some operator matrices.

Key words: Moore-Penrose inverse, idempotent operator, Hilbert space, Moore-Penrose inverse, idempotent operator

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