| 引用本文： |
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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. [点击复制]
- LI Da-lin,HUANG Xue-yan.On the Uniqueness of Generalized Eigenmatrices[J].Guangxi Sciences,2008,15(3):228-230,234. [点击复制]
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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. |
| 关键词: 矩阵 广义特征矩阵 若当标准型 若当链 Toeplitz子阵 |
| DOI： |
| 投稿时间：2007-09-21 |
| 基金项目:广西教育厅科研项目(200707LZ259)资助 |
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| On the Uniqueness of Generalized Eigenmatrices |
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LI Da-lin1, HUANG Xue-yan2
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| (1.Department of Basic Courses, Liuzhou Vocational Institute of Technology, Liuzhou, Guangxi, 545006, China;2.Department of Mathematics and Computer Science, Qinzhou College, Qinzhou, Guangxi, 535000, China) |
| 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. |
| Key words: matrix generalized eigenmatrix Jordan canonical form Jordan chain Toeplitz block submatrix |
