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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (4): 43-48.doi: 10.6040/j.issn.1671-9352.0.2015.114

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广义投影算子和超广义投影算子的一些新刻画

罗高骏,周良,左可正*   

  1. 湖北师范学院数学与统计学院, 湖北 黄石 435002
  • 收稿日期:2015-03-18 出版日期:2016-04-20 发布日期:2016-04-08
  • 通讯作者: 左可正(1962— ),男,教授,研究方向为代数与矩阵分析. E-mail:xiangzuo28@163.com E-mail:a446761001@163.com
  • 作者简介:罗高骏(1990— ),男,硕士,研究方向为矩阵分析及应用. E-mail:a446761001@163.com
  • 基金资助:
    国家自然科学基金资助项目(11271105);湖北省教育厅重点资助项目(D20122202)

Some new characterizations of generalized and hypergeneralized projectors

LUO Gao-jun, ZHOU Liang, ZUO Ke-zheng*   

  1. Department of Mathematics, Hubei Normal University, Huangshi 435002, Hubei, China
  • Received:2015-03-18 Online:2016-04-20 Published:2016-04-08

摘要: 运用矩阵的ΣKL分解及相关矩阵的特征,研究了广义投影算子(A2=A*)和超广义投影算子(A2=A)的性质,得到了一些新的刻画,这些结果推广了Baksalary的相关结果。

关键词: Mooer-Penrose逆, 群逆, 超广义投影算子, 广义投影算子

Abstract: The paper mainly uses the decomposition of the ΣKL of the matrix to give several new characteristics of generalized projectors(A2=A*)and hypergeneralized projectors(A2=A), which generalized some related results of Baksalary.

Key words: the mooer-penrose inverse, generalized projectors, group inverse, hypergeneralized projectors

中图分类号: 

  • O152.2
[1] WANG Guorong, WEI Yimin, QIAO Sanzheng. Generalized inverses: theory and computations[M]. Beijing: Science Press, 2004.
[2] BEN-ISRAEL A, GREVILLE T N E. Generalized inverses[M]. New York: Springer-Verlag, 2003.
[3] GROB J, TRENKLER G. Generalized and hypergeneralized projectors[J]. Linear Algebra and Its Applications, 1997, 264:463-474.
[4] BAKSALARY J K, LIU Xiaoji. An alternative characterization of generalized projectors [J]. Linear Algebra and Its Applications, 2004, 388:61-65.
[5] BAKSALARY J K, BAKSALARY O M, LIU Xiaoji. Further properties of generalized and hypergeneralized projectors [J]. Linear Algebra and Its Applications, 2004, 389:295-303.
[6] BAKSALARY J K, BAKSALARY O M, LIU Xiaoji. Further results on generalized and hypergeneralized projectors[J]. Linear Algebra and Its Applications, 2008, 429:1038-1050.
[7] BAKSALARY O M. Revisitation of generalized and hypergeneralized projectors[C] // Statistical Inference, Econometric Analysis and Matrix Algebra: Festschrift in Honour of G(¨overo)tz Trenkler. New York: Springer-Verlag, 2008: 317-324.
[8] HARTWIG R E, SPINDELB(¨overO)CK K. Matrices for which A* and A commute[J]. Linear and Multilinear Algebra, 1984, 14:241-256.
[9] BAKSALARY O M, TRENKLER G. On a generalized core inverse[J]. Applied Mathematics and Computation, 2014, 236:450-457.
[10] BAKSALARY O M, STYAN G P H, TRENKLER G. On a matrix decomposition of Hartwig and Spindelb(¨overo)ck[J]. Linear Algebra and Its Applications, 2009, 430(10):2798-2812.
[1] 李静,何承源. 求解首尾差循环矩阵逆与广义逆的快速算法[J]. J4, 2013, 48(6): 96-99.
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