线性矩阵方程组AX=B,YA=D的最小二乘(R,Sσ)-交换解

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线性矩阵方程组AX=B,YA=D的最小二乘(R,S_σ)-交换解

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线性矩阵方程组AX=B,YA=D的最小二乘(R,S_σ)-交换解文娅琼¹, 李姣芬², 黎稳³1. 桂林电子科技大学数学与计算科学学院桂林 541004;
2. 桂林电子科技大学数学与计算科学学院广西高校数据分析与计算重点实验室桂林 541004;
3. 华南师范大学数学科学学院广州 510631 The Least-square Solutions to the Linear Matrix Equations AX=B, YA=D with (R,S_σ)-commutative Matrices Ya Qiong WEN¹, Jiao Fen LI², Wen LI³1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China;
2. School of Mathematics and Computational Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, P. R. China;
3. School of Mathematical Sciences, South China Normal University, China 510631, P. R. China

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摘要Trench在[Characterization and properties of（R，S_σ）-commutative matrices， Linear Algebra Appl.，2012， 436:4261-4278]中给出了（R，S_σ）-交换矩阵的定义.本文在此基础上讨论（R，S_σ）-交换矩阵的一般性结构，对给定的矩阵X，Y，B，D，以及线性方程组AX=B，YA=D在（R，S_σ）-交换矩阵集合中的最小二乘问题及最佳逼近问题.细致分析最小二乘（R，S_σ）-交换解和最佳逼近解的具体解析表达式.同时在方程组相容情况下分析（R，S_σ）-交换解存在的充要条件及其具体解析表达式.

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收稿日期: 2018-11-19

MR (2010):

O177.2

基金资助:国家自然科学基金资助项目（11761024，11561015，11671158，U1811464）；广西自然科学基金资助项目（2016GXNSFAA380074，2016GXNSFFA380009，2017GXNSFBA198082）；桂林电子科技大学研究生优秀学位论文培育项目（17YJPYSS24）

通讯作者:李姣芬E-mail: lixiaogui1290@163.com

作者简介: 黎稳,E-mail:liwen@scnu.edu.cn

引用本文:

文娅琼, 李姣芬, 黎稳. 线性矩阵方程组AX=B,YA=D的最小二乘(R,S_σ)-交换解[J]. 数学学报, 2019, 62(6): 833-852. Ya Qiong WEN, Jiao Fen LI, Wen LI. The Least-square Solutions to the Linear Matrix Equations AX=B, YA=D with (R,S_σ)-commutative Matrices. Acta Mathematica Sinica, Chinese Series, 2019, 62(6): 833-852.

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