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

被引：6

作者：

Zhang, Huiting ^{[1
]}

Liu, Lina ^{[1
]}

Liu, Hao ^{[2
]}

Yuan, Yongxin ^{[1
]}

机构：

[1] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 418卷

关键词：

Spectral decomposition; Singular value decomposition; Column unitary matrix; Optimal approximation; LEAST-SQUARES SOLUTIONS; REFLEXIVE SOLUTIONS; POSITIVE SOLUTIONS;

D O I：

10.1016/j.amc.2021.126789

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 = I-p 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. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：9

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