The reverse order law for the weighted least square $ g $-inverse of multiple matrix products

Baifeng Qiu; Zhiping Xiong; Baifeng Qiu; Zhiping Xiong

doi:10.3934/math.20231494

AIMS Mathematics

2023, Volume 8, Issue 12: 29171-29181. doi: 10.3934/math.20231494

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The reverse order law for the weighted least square $ g $-inverse of multiple matrix products

Baifeng Qiu ,
Zhiping Xiong ^,

School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, Guangdong, China

Received: 02 September 2023 Revised: 09 October 2023 Accepted: 15 October 2023 Published: 26 October 2023
MSC : 47A05, 15A09, 15A24

By using the ranks of the generalized Schur complement, the equivalent conditions for reverse order laws of the $ \{1, 3M\}- $ and the $ \{1, 4N\}- $ inverses of the multiple product of matrices are derived.
- reverse order law,
- weighted least square $ g $-inverse,
- matrix product,
- generalized Schur complement,
- maximal and minimal ranks
Citation: Baifeng Qiu, Zhiping Xiong. The reverse order law for the weighted least square $ g $-inverse of multiple matrix products[J]. AIMS Mathematics, 2023, 8(12): 29171-29181. doi: 10.3934/math.20231494

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Abstract

By using the ranks of the generalized Schur complement, the equivalent conditions for reverse order laws of the $ \{1, 3M\}- $ and the $ \{1, 4N\}- $ inverses of the multiple product of matrices are derived.

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