【摘要】 本文考虑矩阵A_n=D_n+B_n特征值反问题。如果给定矩阵A_n的特征值为λ₁,λ₂,…,λ_n,本文证明了A_n的对角元α₁,α₂,…,α_n恰好为一个n阶多项式的n个根,而这个n阶多项式的系数都可以由矩阵A_n的特征值λ₁,λ₂,…,λ_n及B_n元素的值算得。更多还原

【Abstract】 In this paper, we consider inverse eigenvalue problem for matrix A_n=D_n+B_n. If λ₁,λ₂,…,λ_n the eignvalues of A_n have been given, it is proved in this paper that α₁, α₂,…,α_n the diagonal elements of A_n are just the n solutions of the n-order polynomial, and its coefficients can be calculated by the eignvalues of A_n, λ₁, λ₂,…,λ_n and the elements of B_n.更多还原