Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (4): 739-744.

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Representations of Drazin Inverse of  Sum for Two Matrices

GUO Li, WANG Anqi, HOU Yu, LUAN Tian   

  1. School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China
  • Received:2022-12-05 Online:2023-07-26 Published:2023-07-26

Abstract: We considered the representation of the Drazin inverses of the sum for two matrices. For n-|th order matrices P and Q, the expression  of the Drazin inverse of the sum for two matrices P+Q was given by using the Cline formula and the properties of Drazin inverse under the conditions such as  P2QP2=0, P3QP=0, PQ3=0, PQ2P=0, P2QPQ=0, etc.

Key words: generalized inverse, Drazin inverse, index

CLC Number: 

  • O151.21