Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1619-1632.

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The Properties and Applications of the MP Weak Core Inverse

Xiaoji Liu(),Mengyue Liao(),Hongwei Jin*()   

  1. School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006
  • Received:2021-12-03 Online:2022-12-26 Published:2022-12-16
  • Contact: Hongwei Jin;;
  • Supported by:
    the National Natural Science Foundation of China(12061015);the Guangxi Natural Science Foundation(2018GXNSFDA281023);the Special Fund for Science and Technological Bases and Talents of Guangxi(桂科AD21220024)


In this paper, the concept of the Moore-Penrose weak Core inverse (MPWC inverse) is proposed based on the Moore-Penrose inverse and the weak Core inverse. It is described from algebraic and geometric perspectives respectively. The relationship between the MP weak Core inverse and the nonsingular bordered matrix is given. The expression of the MP weak Core inverse is given by using the Hartwig-Spindelböck decomposition and the Core-EP decomposition. The equivalence between the MP weak Core inverse of a matrix and EP matrix, the characterization and the perturbation analysis are given.

Key words: Weak Core inverse, Moore-Penrose inverse, MPWC inverse, Core-EP decomposition

CLC Number: 

  • O151