| 广义四元数矩阵方程AX-DXB=R |
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| 引用本文： | 李样明. 广义四元数矩阵方程AX-DXB=R[J]. 数学杂志, 2002, 22(3): 281-286 |
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| 作者姓名： | 李样明 |
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| 作者单位： | 广东教育学院数学系,广州,510303,中山大学数学系,广州,510275 |
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| 摘 要： | 设HF为域F上的广义四元数除环，ChF≠2。本文利用拟线性变换T（X）＝AX－DXB讨论HF上矩阵方程AX－DXB＝R的求解问题，获得了上方程存在（唯一）解的几个充分必要条件，并给出了解的显式公式。
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| 关 键 词： | 广义四元数矩阵 矩阵方程 表示矩阵 |
THE GENERALIZED QUATERNION MATRIX EQUATION AX DXB = R |
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| LI Yang-ming. THE GENERALIZED QUATERNION MATRIX EQUATION AX DXB = R[J]. Journal of Mathematics, 2002, 22(3): 281-286 |
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| Authors: | LI Yang-ming |
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| Abstract: | Let HF be the generalized quaternion division algebra over a field F with Char F≠ 2. In this paper, the matrix equation AX-DXB = R over Hf is considered. By using thequasilinear transformation T (X)= AX- DXB, this paper obtains several necessary andsufficient conditions for the existence of a solution or a unique solution to the matrix equation,and gives some explicit formulas of solutions. |
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| Keywords: | Matrix generalized quaternion matrix Matrix equation Representation matrix |
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