The solution of the matrix equation AXB=D and the system of matrix equations AX=C,XB=D with X*X=Ip

Huiting Zhang, Lina Liu, Hao Liu and Yongxin Yuan

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: In this paper, the solvability conditions for the matrix equation AXB=D and a pair of matrix equations AX=C,XB=D with the constraint X*X=Ip are deduced by applying the spectral and singular value decompositions of matrices, and the expressions of the general solutions to these matrix equations are also provided. Furthermore, the associated optimal approximate problems to the given matrices are discussed and the optimal approximate solutions are derived. Finally, two numerical experiments are given to validate the accuracy of the results.

Keywords: Spectral decomposition; Singular value decomposition; Column unitary matrix; Optimal approximation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008717

DOI: 10.1016/j.amc.2021.126789

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