几种矩阵逆的连续性  

On the continuity of several kinds of matrices inverse

作　　者：吴池业[1] 黄廷祝[1] 

机构地区：[1]电子科技大学应用数学学院,四川成都610054

出　　处：《纯粹数学与应用数学》2009年第3期481-485,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金(10771030);教育部科学技术研究重点项目(107098);四川省应用基础研究项目(2008JY0052);高等学校博士点专项科研基金(20070614001);电子科技大学"中青年学术带头人+创新团队"项目

摘　　要：非奇异矩阵的逆是矩阵元素的连续函数.学者们也对矩阵广义逆的连续性有所研究.本文应用矩阵分裂和两个矩阵之和的逆的展开式,给出了一般非奇异矩阵,M-矩阵和H-矩阵的逆的连续性.当一些合理的条件满足时,这几种矩阵的逆是连续的.The inverse of a nonsingular matrix is a continuous function of the elements of the matrix. The continuity of the generalized inverse A＋ of a matrix A was also investigated by scholars. In this paper, applying matrices splitting and the expansion of inverse of sum of two matrices, the continuity of matrices inverse, such as general nonsingular matrices, M-matrices and H-matrices, respectively, is provided. Inverses of these matrices are continuous when some reasonable conditions are satisfied.

关 键 词：连续性 矩阵逆 M-矩阵 H-矩阵 广义逆 

分 类 号：O241.6[理学—计算数学]