The present paper is devoted to characterizing the weak core inverse and the weak core matrix using the core-EP decomposition. Some new characterizations of the weak core inverse are presented by using its range space, null space and matrix equations. Additionally, we give several new representations and properties of the weak core inverse. Finally, we consider several equivalent conditions for a matrix to be a weak core matrix.
Citation: Zhimei Fu, Kezheng Zuo, Yang Chen. Further characterizations of the weak core inverse of matrices and the weak core matrix[J]. AIMS Mathematics, 2022, 7(3): 3630-3647. doi: 10.3934/math.2022200
The present paper is devoted to characterizing the weak core inverse and the weak core matrix using the core-EP decomposition. Some new characterizations of the weak core inverse are presented by using its range space, null space and matrix equations. Additionally, we give several new representations and properties of the weak core inverse. Finally, we consider several equivalent conditions for a matrix to be a weak core matrix.
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Zhimei Fu, Kezheng Zuo, Yang Chen. Further characterizations of the weak core inverse of matrices and the weak core matrix[J]. AIMS Mathematics, 2022, 7(3): 3630-3647. doi: 10.3934/math.2022200
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