| 广义特征矩阵的唯一性 |
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| 引用本文： | 李大林,黄雪燕.广义特征矩阵的唯一性[J].广西科学,2008,15(3):228-230,234. |
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| 作者姓名： | 李大林 黄雪燕 |
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| 作者单位： | 1. 柳州职业技术学院基础部,广西柳州,545006
2. 钦州学院数学与计算机科学系,广西钦州,535000 |
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| 摘 要： | 利用广义特征向量的深度,获得极大若当链的一般形式,并推导出在满足PJP-1=SJS-1的2个可逆矩阵P和S之间存在一个主对角线上具有上三角分块Toeplitz子阵的可逆矩阵H,使得S=PH,从而证明广义特征矩阵的唯一性.
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| 关 键 词： | 矩阵 广义特征矩阵 若当标准型 若当链 Toeplitz子阵 |
| 收稿时间： | 2007/9/21 0:00:00 |
On the Uniqueness of Generalized Eigenmatrices |
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| LI Da-lin and HUANG Xue-yan.On the Uniqueness of Generalized Eigenmatrices[J].Guangxi Sciences,2008,15(3):228-230,234. |
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| Authors: | LI Da-lin and HUANG Xue-yan |
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| Institution: | Department of Basic Courses, Liuzhou Vocational Institute of Technology, Liuzhou, Guangxi, 545006, China and Department of Mathematics and Computer Science, Qinzhou College, Qinzhou, Guangxi, 535000, China |
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| Abstract: | The general form of the maximal Jordan chains of the defective matrix is getten with the notation of depths of the generalized eigenvectors.For two invertible matrices P and S such that PJP-1=SJS-1,we find that there exists a block matrix H with upper triangular Toeplitz block matrices laying on its principal block diagonal such that S = PH,which allows to prove the uniqueness of generalized eigenmatrices. |
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| Keywords: | matrix generalized eigenmatrix Jordan canonical form Jordan chain Toeplitz block submatrix |
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