Brualdi定理的推广及其应用

A generalization of Brualdi's theorem and its applications

引入回路α 对角占优矩阵和矩阵的无向连通性概念,推广了关于不可约矩阵非奇异性的Brualdi定理,得到回路α 对角占优矩阵为H 矩阵的充要条件.作为应用,对经典的Ostrowski和Brualdi关于矩阵特征值的分布区域作了讨论.

In this paper, the concepts of circuit α-diagonal dominant matrices and undirected connectedness of matrices are introduced; the classical Brualdi's results for the nonsingularity of matrices are extended; some necessary and sufficient conditions for a circuit α-diagonal dominant matrix to be an H-matrix are obtained. As their applications, the classical Ostrowski's theorem and Brauldi's theorem for the inclusion regions of eigenvalues of a matrix are carefully discussed.