广义Jacobi矩阵的逆特征问题  

Inverse Eigenproblem of Generalized Jacobi Mathix

作　　者：冯立超[1,2] 

机构地区：[1]华中科技大学数学与统计学院,湖北武汉430074 [2]河北理工大学理学院,河北唐山063009

出　　处：《应用数学》2008年第S1期20-24,共5页Mathematica Applicata

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.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.

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 

分 类 号：O151.21[理学—数学]