The {1,2,3,1m}-inverses: A generalization of core inverses for matrices
作者：
Highlights：
• In this paper, for any complex square matrix A (with index m), we introduce the new concept of {1,2,3,1m}-inverses as a generalization of the core inverse. The set of all {1,2,3,1m}-inverses of a matrix is described.
• It is proved that A has a unique {1,2,3,1m}-inverse for some m if and only if it has index 0 or 1, in which case the core inverse is exactly its unique {1,2,3,1m}-inverse.
• EP properties of matrices are characterized by using {1,2,3,1m}-inverses.
摘要
•In this paper, for any complex square matrix A (with index m), we introduce the new concept of {1,2,3,1m}-inverses as a generalization of the core inverse. The set of all {1,2,3,1m}-inverses of a matrix is described.•It is proved that A has a unique {1,2,3,1m}-inverse for some m if and only if it has index 0 or 1, in which case the core inverse is exactly its unique {1,2,3,1m}-inverse.•EP properties of matrices are characterized by using {1,2,3,1m}-inverses.
论文关键词：Moore-Penrose inverse,Drazin inverse,Core inverse,{1,2,3,1m}-inverse,EP matrix
论文评审过程：Received 30 October 2021, Revised 21 January 2022, Accepted 1 April 2022, Available online 19 April 2022, Version of Record 19 April 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127149
