主理想环上矩阵方程AX=B的对称解  

The Symmetric Solution of Matrix Equation AX=B on Principal Ideal Ring

作　　者：张四保 邓勇 ZHANG Si-bao;DENG Yong(College of Mathematics and Statistics,Kashi University,Kashi 844008,China)

机构地区：[1]喀什大学数学与统计学院,喀什844008

出　　处：《科学技术与工程》2020年第25期10133-10137,共5页Science Technology and Engineering

基　　金：新疆维吾尔自治区自然科学基金(2017D01A13);云南省教育厅项目(2019J1182)。

摘　　要：研究了主理想环R上的矩阵方程AX=B存在对称解的条件及解的结构,推出了其在R上有对称解的充分必要条件是它在R上有解且矩阵AB T对称。并在矩阵方程AX=B存在对称解的条件下,给出了其通解的构造方法。The conditions for the existence of symmetric solutions of matrix equation AX=B over the principal ideal ring R and the structure of solutions were studied.The necessary and sufficient condition for the existence of symmetric solutions of matrix equation AX=B over the principal ideal ring R is that it has solutions on R and the matrix AB T is symmetric.Moreover,under the condition that the matrix equation AX=B had a symmetric solution,the construction method of its general solution was given.

关 键 词：主理想环 矩阵方程 对称解 解的结构 

分 类 号：O151[理学—数学]