The solutions of two classes of dual matrix equations

Yinlan Chen; Min Zeng; Ranran Fan; Yongxin Yuan; Yinlan Chen; Min Zeng; Ranran Fan; Yongxin Yuan

doi:10.3934/math.20231171

AIMS Mathematics

2023, Volume 8, Issue 10: 23016-23031. doi: 10.3934/math.20231171

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The solutions of two classes of dual matrix equations

School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

Received: 23 May 2023 Revised: 28 June 2023 Accepted: 04 July 2023 Published: 19 July 2023
MSC : 15A24, 65F05

The solvability conditions for the dual matrix equation $ AXB = D $ and a pair of dual matrix equations $ AX = C $ and $ XB = D $ are deduced by applying the singular value decomposition, and the expressions of the general solutions to these dual matrix equations are provided. Furthermore, the minimum-norm solutions of these dual matrix equations are provided. Finally, two numerical experiments are given to validate the accuracy of the results obtained.
- dual matrix equation,
- singular value decomposition,
- general solution,
- minimum-norm solution
Citation: Yinlan Chen, Min Zeng, Ranran Fan, Yongxin Yuan. The solutions of two classes of dual matrix equations[J]. AIMS Mathematics, 2023, 8(10): 23016-23031. doi: 10.3934/math.20231171

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Abstract

The solvability conditions for the dual matrix equation $ AXB = D $ and a pair of dual matrix equations $ AX = C $ and $ XB = D $ are deduced by applying the singular value decomposition, and the expressions of the general solutions to these dual matrix equations are provided. Furthermore, the minimum-norm solutions of these dual matrix equations are provided. Finally, two numerical experiments are given to validate the accuracy of the results obtained.

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