| 四元数体上方阵的标准形与矩阵方程AX＋XB=D |
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| 引用本文： | 黄礼平.四元数体上方阵的标准形与矩阵方程AX＋XB=D[J].新疆大学学报(理工版),1994,11(1):35-38,59. |
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| 作者姓名： | 黄礼平 |
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| 作者单位： | 湘潭矿业学院基础课部 |
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| 摘 要： | 本文简明地证明了任一个四元数方阵相似于一个唯一的Ｊｏｒｄａｎ标准形，得到关于四元数矩阵方程ＡＸ—ＸＢ＝Ｄ的可解性的两个判别准则，并推广Ｗ．Ｅ．Ｒｏｔｈ定理到四元数体．
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| 关 键 词： | Jordan标准形 四元数 矩阵方程 |
Canonical Form or Square Matrix and Matrices Equation AX+XB=Dover Quaternion Field |
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| Huang Liping.Canonical Form or Square Matrix and Matrices Equation AX+XB=Dover Quaternion Field[J].Journal of Xinjiang University(Science & Engineering),1994,11(1):35-38,59. |
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| Authors: | Huang Liping |
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| Abstract: | This paper succinctly proves that every quaternion square matrix is similar to a unique Jordan canonical form,obtains two criterions for solvability of quaternions matrices equation AX+XB=D, and extends the W. E. Roth's theorem to the quaternion field. |
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| Keywords: | quaternions matrices right eigenvalues Jordan canonical form quaternions matrices equation |
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