| 摘要: |
| 给出一种用广义特征矩阵计算若当基的方法.该方法在获得亏损矩阵的特征值及其代数重数的基础上,求出广义特征矩阵,利用系列广义特征矩阵构成分块矩阵,并使每一分块矩阵正好是特征向量或广义特征向量,再施以初等变换求出若当基. |
| 关键词: 亏损矩阵 相似变换矩阵 广义特征矩阵 若当标准形 若当链 |
| DOI： |
| 投稿时间：2012-04-07 |
| 基金项目:广西教育厅科研项目(201106LX751)资助。 |
|
| Computation of Jordan Bases by Generalized Eigenmatrices |
|
LI Da-lin1, HUANG Xiao-yu2
|
| (1.Department of Basic Courses, Liuzhou Vocational Institute of Technology, Liuzhou, Guangxi, 545006, China;2.Department of Humanities, Guangxi Technological College of Machinery and Electricity, Nanning, Guangxi, 530007, China) |
| Abstract: |
| A new algorithm is given to compute the transition matrix to transform the defective matrix into Jordan canonical form. The basic information that are easily obtained, such as the eigenvalues and their algebraic multiplicities, are used to generalize matrices, where their nontrivial column vectors are eigenvectors or generalized eigenvectors. They constitute a block matrix, from which all information of Jordan canonical form can be obtained by means of column elementary transformations. |
| Key words: defective matrix similarity transition matrix generalized eigenmatrix Jordan canonical form Jordan chain |
