逆特征问题的某些有趣性质

Some Interesting Properties on the Inverse Eigenproblem

证明了下面两种有趣性质：（１）如果三对角对称正定阵的逆特征问题有唯一解，则三对角对称阵的逆特征问题有唯一解；（２）如果Ｊａｃｏｂｉａｎ矩阵的逆特征问题有唯一解，则三对角对称阵的逆特征问题有唯一解．

The following two interesting properties are proved:(1)If the inverse eigenproblem for tridiagonal symmetric positive definite matrices has a unique solution,then the inverse eigenproblem for tridiagonal symmetric matrices has a unique solution;(2)If the inverse eigenproblem for Jacobian matrices has a unique solution,then inverse eigenproblem for tridiagonal symmetric matrices has a unique solution.