| 主理想环上矩阵方程AX=B的对称解 |
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| 引用本文： | 张四保,邓勇. 主理想环上矩阵方程AX=B的对称解[J]. 科学技术与工程, 2020, 20(25): 10133-10137 |
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| 作者姓名： | 张四保 邓勇 |
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| 作者单位： | 喀什大学数学与统计学院,喀什844008 |
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| 基金项目： | 新疆维吾尔自治区自然科学基金（2017D01A13）；云南省教育厅基金（2019J1182） |
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| 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ABT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.
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| 关 键 词： | 主理想环 矩阵方程 对称解 解的结构 |
| 收稿时间： | 2020-02-17 |
| 修稿时间： | 2020-06-12 |
The Symmetric Solution of Matrix Equation AX=B on Principal Ideal Ring |
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| ZHANG Sibao. The Symmetric Solution of Matrix Equation AX=B on Principal Ideal Ring[J]. Science Technology and Engineering, 2020, 20(25): 10133-10137 |
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| Authors: | ZHANG Sibao |
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| Affiliation: | College of Mathematics and Statistics, Kashi University |
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| Abstract: | The conditions for the existence of symmetric solutions of matrix equation AX=B over the principal ideal ring R and the structure of solutions are 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 ABT is symmetric. Moreover, under the condition that the matrix equation AX=B has a symmetric solution; the construction method of its general solution is given. |
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| Keywords: | principal ideal ring the matrix equation symmetric solution |
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