华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (4): 35-42.doi: 10.3969/j.issn.1000-5641.2023.04.004

• 数学 • 上一篇    下一篇

{A,W}加权核-EP分解下的矩阵加权Drazin逆的刻画与表示

胡春梅()   

  1. 丽江师范高等专科学校 数学与信息技术学院, 云南 丽江　674199
  • 收稿日期:2021-11-26 出版日期:2023-07-25 发布日期:2023-07-25
  • 作者简介:胡春梅, 女, 硕士, 讲师, 研究方向为矩阵和算子广义逆的理论及其应用.E-mail: chunmeihu2008@163.com
  • 基金资助:
    云南省教育厅科学研究基金(2021J1149)

Characterization and representation of weighted Drazin inverse of matrices based on weighted core-EP decomposition of the pair {A,W}

Chunmei HU()   

  1. School of Mathematics and Information Technology, Lijiang Teachers College, Lijiang, Yunnan　674199, China
  • Received:2021-11-26 Online:2023-07-25 Published:2023-07-25

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摘要：

主要讨论 $\{A, W\}$ 加权核-EP分解下的矩阵加权Drazin逆 $A^{d, W}$ . 将矩阵对 $\{A, W\}$ 进行核-EP分解, 得到 $A^{d, W}$ 的刻画, 进而推导出 $A^{d, W}$ 的表示. 最后讨论了 $A^{d, W}$ 的极限表示和积分表示, 并给出一个算例.

关键词: 加权Drazin逆, 加权核-EP分解, 极限表示, 积分表示

Abstract:

This paper presents an investigation of the weighted Drazin inverse $A^{d, W}$ of matrices based on the weighted core-EP decomposition of the pair $\{A, W\}$ . Some characterizations and representations of the weighted Drazin inverse are presented using the weighted core-EP decomposition of the pair $\{A, W\}$ . Further, the limit representations and the integral representations of the weighted Drazin inverse are discussed. Furthermore, an example is presented.

Key words: weighted Drazin inverse, weighted core-EP decomposition, limit representation, integral representation

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