期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

1×2算子矩阵的Moore-Penrose逆 被引量：4

Moore-Penrose inverses of 1×2 operator matrices
下载PDF
导出
摘要 设A1、A2是Hilbert空间H上的两个有界线性算子,利用算子分块技巧研究了1×2算子矩阵(A1 A2)作为从H⊙H到H上的算子Moore-Penrose逆,当R(A1)∩R(A2)={0}和R(A1)■R(A2)⊥时,给出了矩阵(A1 A2)的Moore-Penrose逆的具体表示. Let A1, A2 be two bounded linear operators on a Hilbert space S. By using the technique of block operator matrix, the Moore-Penrose inverse of a 1 × 2 operator matrix （A 1 A2 ） is studied, where （A 1 A a） is an operator from H＋H into H. An explict representation of the Moore-Penrose inverse of （A1 A2） is given, when R（A1）∩R（A2）= {0} or R（A1） lohtain in R（A2）^⊥.
作者 许俊莲 杜鸿科
机构地区 陕西师范大学数学与信息科学学院
出处 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第2期11-14,共4页 Journal of Shaanxi Normal University：Natural Science Edition
基金 国家自然科学基金资助项目(10571113)
关键词 算子矩阵 广义逆 Moore—Penrose逆 正交投影 operator matrix generalized inverse Moore-Penrose inverse orthogonal projection
分类号 O177.1 [理学—基础数学]
  • 相关文献

参考文献8

  • 1Israel A B, Greville T N E. Generalized inverse: theory and applications[M].2nd ed. New York: Springer-Verlag, 2003.
  • 2Israel A B. The Moore of the Moore-Penrose inverse[J ]. Linear Algebra (Electron), 2002, 9: 150-157.
  • 3Cegielsld A. Obtuse cones and Gram matrices with nonnegative inverse[J]. Linear Algebra and its Applications, 2001, 335: 167-181.
  • 4Moore E H. On the reciprocal of the genera algebraicmatrix[J ]. Bulletin of the American Mathematical Societv, 1920, 26: 394-395.
  • 5Penrose R, A generalized inverse for matrices[J].Mathematical Proceedings of the Cambridge Philosophical Society, 1955, 51:406-413.
  • 6Baksalary J. K, Baksalary O. M. Particular formulae for the Moore-Penrose inverse of a columnwise partitiones matrix[J].Linear Algebra and its Applications, 2007,421:16-23.
  • 7DU H K, Deng C Y. A new characterization of gaps between two subspaces[J]. Proceedings of the American Mathematical Society, 2005, 133:3 065-3070.
  • 8Douglas R G. On majorization, factorization and range inclusion of operators in a Hilbert space[J]. Proceedings of the American Mathematical Society, 1966, 17: 413-416.

同被引文献29

  • 1ARONSZAJN N, SMITH K T. Invariant subspaces of completely continuous operators [J]. Annals of Mathematics, 1954, 60: 345-350.
  • 2HOLBRLLK J, NORDREN F, RADJARI H, et al. On the operator equation AX = XAX I-J]. Linear Algebra and its Applications, 1999, 295 113-116.
  • 3CONWAY J B. A Course in Functional Analysis [M]. New York: Springer-Verlag, 1990.
  • 4CLINE R E. Representations for the generalized inverse of a partitioned matrix[J], Journal of the Society for Industrial and Applied Mathematics, 1964, 12: 588-600.
  • 5BRADEN H. The equations A^TX ± X^TA = B[ J ]. Matrix Anal Appl, 1998, 20:295-302.
  • 6XU Qingxiang, SHENG Lijuan, GU Yangyang. The solutions to some operator equations [ J ]. Linear Algebra and its applica- tions, 2008, 429 : 1997-2024.
  • 7BHATIA R. Matrix analysis [M]. New York: Springer-Verlag, 1997.
  • 8CONWAY J B. A course in functional analysis[M]. New York: Springer-Verlag, 1990.
  • 9BEN I A. The Moore of the Moore-Penrose inverse [J]. Electronic Journal of Linear Algebra, 2002, 9:150-157.
  • 10FILLMORE L R, WILLIAMS J P. On operator ranges[J]. Advances in Mathematics, 1971, 7: 254-281.

引证文献4

二级引证文献3

陕西师范大学学报（自然科学版）
2008年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部