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

作者：

Highlights：

• The column unitary solutions to the matrix equation AXB=D and the system of matrix equations AX=C,XB=D are considered.

• The solvability conditions for the existence and the explicit expressions for the general solution are obtained.

• Simple recipes for the numerical computations are provided.

摘要

•The column unitary solutions to the matrix equation AXB=D and the system of matrix equations AX=C,XB=D are considered.•The solvability conditions for the existence and the explicit expressions for the general solution are obtained.•Simple recipes for the numerical computations are provided.

论文关键词：Spectral decomposition,Singular value decomposition,Column unitary matrix,Optimal approximation

论文评审过程：Received 23 March 2021, Revised 21 October 2021, Accepted 10 November 2021, Available online 5 December 2021, Version of Record 5 December 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126789