| 用奇异值分解方法计算具有重特征值矩阵的特征矢量 |
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| 引用本文： | 迟彬,叶庆凯. 用奇异值分解方法计算具有重特征值矩阵的特征矢量[J]. 应用数学和力学, 2004, 25(3): 233-238 |
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| 作者姓名： | 迟彬 叶庆凯 |
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| 作者单位： | 北京大学 力学与工程科学系,北京 100871 |
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| 基金项目： | 国家自然科学基金资助项目(69974003)，高等院校博士点基金资助项目(2001001011) |
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| 摘 要： | 若当(Jordan)形是矩阵在相似条件下的一个标准形，在代数理论及其工程应用中都具有十分重要的意义．针对具有重特征值的矩阵，提出了一种运用奇异值分解方法计算它的特征矢量及若当形的算法．大量数值例子的计算结果表明，该算法在求解具有重特征值的矩阵的特征矢量及若当形上效果良好，优于商用软件MATLAB和MATHEMATICA．
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| 关 键 词： | 重特征值 特征矢量 特征矢量链 若当形 |
| 文章编号： | 1000-0887(2004)03-0233-06 |
| 收稿时间： | 2002-03-26 |
| 修稿时间： | 2002-03-26 |
Computing the Eigenvectors of a Matrix With Multiplex Eigenvalues by SVD Method |
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| CHI Bin,YE Qing-kai. Computing the Eigenvectors of a Matrix With Multiplex Eigenvalues by SVD Method[J]. Applied Mathematics and Mechanics, 2004, 25(3): 233-238 |
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| Authors: | CHI Bin YE Qing-kai |
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| Affiliation: | Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China |
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| Abstract: | Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA. |
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| Keywords: | multiplex eigenvalue eigenvector eigenvector chain Jordan canonical form |
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