摘要
非负矩阵逆特征值问题的理论兴趣和应用背景一直是热门的研究课题.文[5]中对n=3的情形,限制在至少有3个零元的不可约非负矩阵类中,给出了具有已知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,同时给出了构造全部解集合的简单而有效的公式.作者对n=4的情形,限制在至少有7个零元(但有非零对角元)的不可约矩阵类中,给出了以已知复数集为谱的非负矩阵逆特征值问题有解的充分条件,并在满足此充分条件的情况下,给出了构造全部解集合的简单而有效的公式.
Since the nonnegative inverse eigenvalue problem had good theoretical interest and applicative background, it always attracted a lot of researchers to work on it. In reference [ 5 ] , we proved the sufficient and necessary conditions for a class of irreducible nonnegative 3 × 3 matrix with at least three zero entries to had the given spectra （including complex eigenvalues） and the given set of diagonal entries, and gave the simple formulas of the solution nonnegative matrices whenever the conditions were satisfied. In the paper, we proved the sufficient conditions for a class of irreducible nonnegative 4 × 4 matrix with nonzero diagonal entries and at least seven zero entries to had the given spectra （including complex eigenvalues）. When the sufficient conditions were satisfied, we gave the simple constructing formulas for the solution nonnegative matrices.
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2009年第4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
特征方程
逆特征值问题
irreducible nonnegative matrix
eigenvalue
eigenequation
inverse eigenvalue problem
