摘要
M-矩阵的Hadamard积是一种特殊的矩阵乘积,具有广泛的重要应用背景,概率统计、经济学、组合论、生物学和社会科学等领域中的许多问题都与它有着密切的联系,受到很多专家学者的关注和研究。首先介绍相关定义和性质,其次应用矩阵特征值包含域定理,结合非奇异M-矩阵的性质及其逆矩阵元素的特点,给出不同情形下2个M-矩阵的Hadamard积的最小特征值的几个新估计式。并用理论分析和算例表明新估计式在某些情况下比现有的估计结果更精确,给出的估计式改进了一些现有的结果。
The Hadamard product of M-matrices is a special kind of multiplication on matrices,which has a widely important range of application background.Some problems have a strong association with it in the fields of probability and statistics, economics, combinatorial theory, biology and the social sci-ences.It has been concerned with research by many experts and scholars.Many definitions and properties are introduced. Then the theorem for localizations of Matrix eigenvalues is used, combining with some properties of nonsingular M-matrices and characteristics of its inverse elements. Hadamard product of two M-matrices is further researched in different situations, and some new estimations of smallest eigenvalue are given. Theoretical analysis and numerical figure showed that these inequalities are more exact than some of the current results in some cases.The estimations obtained improve the existing results.
出处
《河北北方学院学报（自然科学版）》
2016年第1期1-7,17,共8页
Journal of Hebei North University:Natural Science Edition
基金
国家自然科学基金支助项目(11261049)
云南省科技厅应用基础研究项目(2013FD052)
文山学院重点学科"数学"建设项目(12WSXK01)
