| 中心代数上一矩阵方程的中心对称与中心斜对称解 |
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| 引用本文： | 王卿文,孙建华,李尚志.中心代数上一矩阵方程的中心对称与中心斜对称解[J].数学季刊,2003,18(2):111-116. |
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| 作者姓名： | 王卿文 孙建华 李尚志 |
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| 作者单位： | Department of Mathematics，University of Science and Technology of China，Hefei 230026，China; Department of Mathematics，University of Yangzhou，Yangzhou 225002，China |
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| 基金项目： | Supported by the Natural Science Foundation of China(10071078)，Supported by the Natural Science Foundation of Shandong Province(Q99A08) |
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| 摘 要： | Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.
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| 关 键 词： | 中心对称解 中心斜对称解 中心代数 矩阵方程 存在性 |
On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra |
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| WANGQing-wen SUNJian-hua LIShang-zhi.On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra[J].Chinese Quarterly Journal of Mathematics,2003,18(2):111-116. |
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| Authors: | WANGQing-wen SUNJian-hua LIShang-zhi |
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| Institution: | [1]DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,China [2]DepartmentofMathematics,UniversityofYangzhou,Yangzhou225002,China |
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| Abstract: | Let Ω be a finite dimensional central algebra and chart Ω≠ 2. The matrix equationAXB - CXD = E over Ω is considered. Necessary and sufficient conditions for the existence ofcentro(skew)symmetric solutions of the matrix equation are given. As a particular case, the matrixequation X - AXB = C over Ω is also considered. |
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| Keywords: | central algebra matrix equation centro( skew) symmetric matrix regular matrix quadruple |
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