摘要
本文通过构造两个具有一定关系的凸集,利用凸集分离原理,给出了判别一个矩阵A不是广义对角占优矩阵的充要条件,即A∈/GDDM的充分必要条件是存在非零向量x≥0,使Ax≤0。从而也得到了M矩阵的一个等价条件。作为该结论的一个应用,进一步得出了可约矩阵为广义对角占优矩阵的充要条件。
Generalized diagonally dominant matrices （GDDM） are widely used in many fields. It is important to determine which matrix is a GDDM. In this paper, we construct two convex sets, then use the separation theory of convex sets to give a necessary and sufficient condition of a matrix to be GDDM, that is, A no belong to GDDM if and only if there exists a nonzero vector x ≥ 0 such that Ax ≤ O. As a consequence, we obtain an equivalent condition for M-matrices. As an application, we also get a necessary and sufficient condition for reducible matrices to be a GDDM.
出处
《工程数学学报》
CSCD
北大核心
2005年第5期947-950,共4页
Chinese Journal of Engineering Mathematics
关键词
广义对角占优矩阵
M矩阵
凸集
generalized diagonally dominant matrix （GDDM）
M-matrix
convex set
