| 四元数矩阵到复矩阵的相似变换 |
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| 引用本文： | 郭时光,王文娟,蔡裕桂.四元数矩阵到复矩阵的相似变换[J].四川理工学院学报(自然科学版),2000,13(4). |
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| 作者姓名： | 郭时光 王文娟 蔡裕桂 |
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| 作者单位： | 四川轻化工学院基础部,四川,自贡,643033 |
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| 摘 要： | 给出四元数体上λ多项式的线性因式分解定理和四元数体上方阵的特征矩阵主法式的存在唯一性定理。用之导出四元数方阵所相似的Jordan形主矩阵的唯一性，四元数矩阵相似于对角形矩阵的一个充要条件及四元数方阵的最小实系数零化多项式的形式。
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| 关 键 词： | λ多项式 主矩阵 主法式 |
Similar Transformation from Quaternion Matrix to Complex One |
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| GUO Shi-guang,WANG Wen-juan,CAI Yu-gui.Similar Transformation from Quaternion Matrix to Complex One[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2000,13(4). |
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| Authors: | GUO Shi-guang WANG Wen-juan CAI Yu-gui |
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| Abstract: | Over quaternionic field, the theorem about the linear factorization ofλ-polynomials and theorem about the existence and uniqueness of the main normal form of an eigenmatrix are given. Then, the follows are gotten: the existence of Jordan form main matrices which are similar to a square matrix, and a necessary and sufficient condition of a matrix similar to a diagonal matrix, and the real coefficient minimum polynomial of a matrix. |
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| Keywords: | λ-polynomial main matrix main normal form matrix |
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