A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $

Huiting Zhang; Hairui Zhang; Lina Liu; Yongxin Yuan; Huiting Zhang; Hairui Zhang; Lina Liu; Yongxin Yuan

doi:10.3934/math.2021156

AIMS Mathematics

2021, Volume 6, Issue 3: 2579-2589. doi: 10.3934/math.2021156

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Research article

A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $

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

Received: 30 October 2020 Accepted: 17 December 2020 Published: 24 December 2020
MSC : 15A09, 15A24

A simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair are provided by the proposed method. Subsequently, the results are applied to determine the solution of the matrix equation $ AXB+GYH = D $ and the Hermitian solution of the matrix equation $ AXB = D. $
- matrix equation,
- generalized inverse,
- common solution,
- Hermitian solution
Citation: Huiting Zhang, Hairui Zhang, Lina Liu, Yongxin Yuan. A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $[J]. AIMS Mathematics, 2021, 6(3): 2579-2589. doi: 10.3934/math.2021156

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Abstract

A simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair are provided by the proposed method. Subsequently, the results are applied to determine the solution of the matrix equation $ AXB+GYH = D $ and the Hermitian solution of the matrix equation $ AXB = D. $

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