| 广义Jacobi矩阵的逆特征问题 |
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| 引用本文： | 冯立超.广义Jacobi矩阵的逆特征问题[J].应用数学,2008(Z1). |
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| 作者姓名： | 冯立超 |
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| 作者单位： | 华中科技大学数学与统计学院;河北理工大学理学院; |
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| 摘 要： | 本文主要讨论广义Jacobi阵及多个特征对的广义Jacobi阵逆特征问题.通过相似变换将广义Jacobi阵变换为三对角对称矩阵,其特征不变、特征向量只作线性变换,再应用前人理论求得广义Jacobi阵元素ai,|bi|,|ci|有唯一解的充要条件及其具体表达式.
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| 关 键 词： | 广义Jacobi阵 逆特征问题 实三对角对称矩阵 Jacobi阵 特征对 |
Inverse Eigenproblem of Generalized Jacobi Mathix |
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| FENG Li-chao.Inverse Eigenproblem of Generalized Jacobi Mathix[J].Mathematica Applicata,2008(Z1). |
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| Authors: | FENG Li-chao |
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| Institution: | 1.School of Mathematics and Statistics;Huazhong University of Science and Technology;Wuhan 430074;China;2.College of Science;Hebei Polytechnic University;Tangshan 063009;China |
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| Abstract: | The paper mainly discusses the generalized Jacobi matrix and its inverse eigenproblem giving some eigen pairs.Generalized Jacobi matrix can be transformed to real tridiagonal symmetric matrix by similar transformation,keeping eigenvalues unchanged and eigenvectors only for linear transformation.Then the necessary and sufficient conditions that the elements of generalized Jacobi matrix are unique can be obtained through the predecessors' theories,moreover,ai,|bi|,|ci|'s specific expressions are gained. |
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| Keywords: | Generalized Jacobi matrix Inverse eigenproblem Real tridiagonal symmetric matrix Jacobi matrix Eigen pair |
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