加法与乘法逆特征值问题的可解性

1.引言 本文讨论如下代数特征值反问题可解的充分条件: 问题A(加法逆特征值问题)。给定一Hermite矩阵A=(a_(ij))_(n×n)及n个实数λ_1,…,λ_n,求一实对角阵D=diag(c_1…,c_n),使得A+D的特征值为λ_1,…,λ_n。 问题M(乘法逆特征值问题)。给定一正定Hermite矩阵A=(a_(ij))_(n×n)和n个正实数

THE SOLUBILITY OF ADDITIVE AND MULTIPLICATIVE INVERSE EIGENVALUE PROBLEMS

With the help of Brouwer's fixed point theorem and the relations of the eigenvalues and diagonal elements of a Hermitian matrix, we give some new sufficient conditions for the sol- ubility of additive and multiplicative inverse eigenvalue problems. Some of F. Laborde's~[3] and Xu Shu-fang's~[5]results can be deduced from our theorems.