Brualdi定理的推广及其应用  

A generalization of Brualdi's theorem and its applications

作　　者：陈神灿[1] 

机构地区：[1]福州大学数学系,福建福州350002

出　　处：《宁夏大学学报（自然科学版）》2003年第4期316-320,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：福建省教育厅基金资助项目(K20025);福州大学科技发展基金资助项目(2003XQ22)

摘　　要：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.

关 键 词：Brualdi定理 回路α-对角占优矩阵 无向连通性 H-矩阵 特征值 谱包含域 

分 类 号：O151.21[理学—数学]