Dual group inverses of dual matrices and their applications in solving systems of linear dual equations

Jin Zhong; Yilin Zhang; Jin Zhong; Yilin Zhang

doi:10.3934/math.2022427

AIMS Mathematics

2022, Volume 7, Issue 5: 7606-7624. doi: 10.3934/math.2022427

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Research article

Dual group inverses of dual matrices and their applications in solving systems of linear dual equations

Jin Zhong ^,,
Yilin Zhang

Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received: 08 December 2021 Revised: 19 January 2022 Accepted: 11 February 2022 Published: 15 February 2022
MSC : 15A09, 15A10

In this paper, we study a kind of dual generalized inverses of dual matrices, which is called the dual group inverse. Some necessary and sufficient conditions for a dual matrix to have the dual group inverse are given. If one of these conditions is satisfied, then compact formulas and efficient methods for the computation of the dual group inverse are given. Moreover, the results of the dual group inverse are applied to solve systems of linear dual equations. The dual group-inverse solution of systems of linear dual equations is introduced. The dual analog of the real least-squares solution and minimal $ P $-norm least-squares solution are obtained. Some numerical examples are provided to illustrate the results obtained.
- dual matrix,
- dual group inverse,
- linear dual equation,
- dual group-inverse solution,
- least-squares solution,
- minimal $ P $-norm least-squares solution
Citation: Jin Zhong, Yilin Zhang. Dual group inverses of dual matrices and their applications in solving systems of linear dual equations[J]. AIMS Mathematics, 2022, 7(5): 7606-7624. doi: 10.3934/math.2022427

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Abstract

In this paper, we study a kind of dual generalized inverses of dual matrices, which is called the dual group inverse. Some necessary and sufficient conditions for a dual matrix to have the dual group inverse are given. If one of these conditions is satisfied, then compact formulas and efficient methods for the computation of the dual group inverse are given. Moreover, the results of the dual group inverse are applied to solve systems of linear dual equations. The dual group-inverse solution of systems of linear dual equations is introduced. The dual analog of the real least-squares solution and minimal $ P $-norm least-squares solution are obtained. Some numerical examples are provided to illustrate the results obtained.

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