| 体上的Sylvester矩阵方程 |
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| 引用本文： | 朱承毅,刘永辉.体上的Sylvester矩阵方程[J].枣庄师专学报,2009,26(2):1-5. |
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| 作者姓名： | 朱承毅 刘永辉 |
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| 作者单位： | 朱承毅,ZHU Cheng-yi(上海财经大学,应用数学系,上海,200433);刘永辉,LIU Yong-hui(上海金融学院,应用数学系,上海,201209)
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| 基金项目： | 上海市教育委员会科技创新项目 |
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| 摘 要： | 通过使用体上矩阵三元组（C，A，B）的联合分解，本文给出了矩阵表达式A—BX—YC的极大和极小秩．作为应用，我们给出了体上的Sylvester矩阵方程BX＋YC=A的一个新的通解公式．利用这个通解公式，我们给出了解集合中解的极大秩和极小秩．
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| 关 键 词： | 体 矩阵组的联合分解 极值秩 Sylvester矩阵方程 |
Slvester matrix equation BX + YC = A over a skew field |
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| ZHU Cheng-yi,LIU Yong-hui.Slvester matrix equation BX + YC = A over a skew field[J].Journal of Zaozhuang Teachers' College,2009,26(2):1-5. |
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| Authors: | ZHU Cheng-yi LIU Yong-hui |
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| Institution: | ZHU Cheng - yi , LIU Yong - hui( 1. Department of Applied Mathematics, Shanghai University of Finance and Economics, Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209 ,China Shanghai 200433, China) |
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| Abstract: | By applying a joint decomposition of triplet matrices （ C, A, B） over a skew field, the extremal ranks of matrix expression A - BX - YC is derived. As applications, we give the general solutions of Slvester matrix equation BX ＋ Y C = A over a skew field. Through the general solutions of BX ＋ YC = A , we derive the extremal ranks of solutions X and Y. |
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| Keywords: | Skew field joint decomposition of triplet matrices extremal rank Slvester matrix equation |
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