摘要
非负矩阵逆特征值问题的提法是:对已知的一个复数组Λ={λ1,…,λn},求一个n×n非负矩阵以Λ为谱.由于非负矩阵逆特征值问题的理论兴趣和应用背景,长期以来,一直吸引不少研究者从事这个热门课题.论文对n=3的情形,限制在至少有三个零元的不可约矩阵类中.首先,给出具有已知的对角元集的非负矩阵逆特征值(包含复特征值)问题有解的充分必要条件;其次,在此基础上,更进一步证明非负矩阵逆特征值问题有解的充分必要条件.在两种情形下都给出了构造全部解集合的简单而有效的公式.
The nonnegative inverse eigenvalue problem is the problem of finding a nonnegative matrix with a given set A of complex numbers as its spectra. Due to its theoretical interest and applicative background, the nonnegative inverse eigenvalue problem always attracts a lot of researchers to work on it. Here we first proved the sufficient and necessary conditions for an irreducible nonnegative 3 × 3 matrix with at least three zero entries to have the given spectra （ including complex eigenvalues） and the given set of diagonal entries. Then we proved the sufficient and necessary conditions for an irreducible nonnegative 3 × 3 matrix with at least three zero entries to have the given set A as its spectra. In both cases, simple formulas of the solution nonnegative matrices were given whenever they exist.
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2008年第5期1-4,共4页
Journal of Anhui University(Natural Science Edition)
基金
安徽大学创新团队基金资助项目
关键词
不可约非负矩阵
特征值
特征多项式
逆特征值问题
irreducible nonnegative matrix
eigenvalue
eigenpolynomial
inverse eigenvalue problem
