| On a Matrix Equation AX＋XB=C over a Skew Field |
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| 引用本文： | 王卿文,秦建国.On a Matrix Equation AX＋XB=C over a Skew Field[J].数学季刊,1993,8(3):97-102. |
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| 作者姓名： | 王卿文 秦建国 |
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| 作者单位： | Changwei Theachers College，Shangqiu Theachers college |
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| 摘 要： | In this paper we study a matrix equation AX BX=C （Ⅰ）over an arbitrary skew field,and give a consistency criterion of （Ⅰ） and an explicit expression of general solutions of （Ⅰ）.A convenient,simple and practical method of solving （Ⅰ） is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.
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| 关 键 词： | 矩阵方程 体 可逆矩阵 一致性 右线性方程齐次系统 基本解系统 |
On a Matrix Equation AX+XB=C over a Skew Field |
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| Wang Qingwen.On a Matrix Equation AX+XB=C over a Skew Field[J].Chinese Quarterly Journal of Mathematics,1993,8(3):97-102. |
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| Authors: | Wang Qingwen |
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| Institution: | [1]ChangweiTheachersCollege [2]ShangqiuTeacherscollege |
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| Abstract: | In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field. |
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| Keywords: | matrix equation over a skew field fundamental system of solutions basic solution matrix subdirect product homogeneous system of right linear equations |
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