带比例矩阵逆特征值问题  

Inverse Eigenvalue Problems for Proportional Matrices

作　　者：易福侠[1] 黄侃[1] YI Fu-xia;HUANG Kan(Department of Fundational Courses,Jiangxi V&T College of Communiction,Nanchang 330013,China)

机构地区：[1]江西交通职业技术学院基础课部,南昌330013

出　　处：《南昌航空大学学报（自然科学版）》2018年第4期40-45,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：江西省教育厅科技项目(GJJ171294)

摘　　要：研究讨论了一类带比例矩阵的特征值反问题:任意给定2n-1(n≥2)个实数λ(n)1<…<λ(2)1<λ(1)1<λ(2)2<…<λ(n)n,求一个带比例矩阵A,使得λ(j)1和λ(j)j分别是其顺序主子阵Aj(1!j!n)的最小和最大特征值。文中给出了此问题有唯一解的充要条件以及有解的充分条件,并给出了解的表达式,最后用数值算例验证了结论的正确性。The inverse eigenvalue problems for a kind of proportional matrix are considered. How to construct a proportional matrix A from the minimal and maximal eigenvalues λ1^(n)<…<λ1^(2)<λ1^(1)<λ2^(2)<…<λn^(n)(2n-1(n≥2)real numbers)of its leading principal submatrices. The necessary and sufficient condition for the unique solutions and the sufficient condition for the solvability of the problems are derived. In addition the expressions are given. Finally,two algorithmic procedures are generated to verify the correctness of conclusions.

关 键 词：带比例矩阵 反问题 最小和最大特征值 

分 类 号：O241.6[理学—计算数学]