低阶双随机矩阵逆特征值问题

对给定的实或复n-重Λ={λ1,…,λn},决定是否存在以Λ为谱的非负方阵的问题称为非负矩阵逆特征值问题,这一直是非负矩阵理论中尚未完全解决的一个研究热点.决定是否存在以Λ为谱的双随机矩阵的问题称为双随机矩阵逆特征值问题,这是既有理论价值、又有实际应用背景的一类非负矩阵逆特征值问题,目前正引起不少学者的兴趣.论文主要研究n(n∈{2,3,4,5})阶双随机矩阵逆特征值问题有解的充分条件,其中给定的Λ={λ1,…,λn}是一般的复n-重,它的全部元素或一部分元素可以是实数.

On the inverse eigenvalue problem for doubly stochastic matrices of a small order

Given an n-tuple Λ,of numbers,real or complex,the problem of deciding the existence of a nonnegative matrix with spectrum Λ is called the nonnegative inverse eigenvalue problem which has long time been one of the problem of main interest in the theory of matrices.The problem of deciding the existence of a doubly stochastic matrix with the given spectrum Λ is called the doubly stochastic inverse eigenvalue problem.The doubly stochastic inverse eigenvalue problem is an important type of nonnegative inverse eigenvalue problems.In the paper,we studied the sufficient conditions for doubly stochastic inverse eigenvalue problem of order two to five to have a solution,where the given spectrum Λ consists of complex numbers all or part of whose elements could be real numbers.