相关矩阵的Hadamard乘积不等式的奇异条件  

Singular conditions for inequalities involving the Hadamard product of correlation matrices

作　　者：林志兴 冯晓霞 杨忠鹏 吕洪斌[3] 陈梅香 LIN Zhixing;FENG Xiaoxia;YANG Zhongpeng;LYU Hongbin;CHEN Meixiang(College of Mathematics and Finance,Putian University,Putian,Fujian 351100,China;College of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China;College of Mathematics and Statistics,Beihua University,Jilin,Jilin 132013,China)

机构地区：[1]莆田学院数学与金融学院,福建莆田351100 [2]闽南师范大学数学与统计学院,福建漳州363000 [3]北华大学数学与统计学院,吉林吉林132013

出　　处：《福州大学学报（自然科学版）》2020年第6期679-684,共6页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61772292);福建省自然科学基金资助项目(2017J01565,2018J01426)。

摘　　要：对相关矩阵R的Hadamard乘积s 1(R)=R °R-2(R-1° R+I)-1(≥0)为奇异的充分且非必要条件,应用半正定矩阵相应不等式的奇异条件和正定矩阵相应的奇异值分解方法,得到了更一般的正定矩阵A,B的s 1(A,B)=A B-(A° I+I °B)(A° B-1+A-1 °B+2 I)-1(A° I+I° B)(≥0)为奇异的充分必要条件.作为应用,得到了s 1(R)为奇异的充分必要条件.As for the sufficient but not necessary condition of Hadamard product s 1(R)=R° R-2(R-1° R+I)-1(≥0)of a correlation matrix R being singular,by applying the singular condition of the corresponding inequalities of positive semi-definite matrices and singular value decomposition of positive definite matrix,it obtains the sufficient and necessary conditions of s 1(A,B)=A B-(A °I+I °B)(A° B-1+A-1 °B+2 I)-1(A °I+I° B)(≥0)being singular,in which A,B are general positive definite matrices.As an application,it gets the sufficient and necessary condition of s 1(R)being singula r as well.

关 键 词：相关矩阵 正定Hermitian矩阵 奇异值分解 HADAMARD乘积 奇异条件 

分 类 号：O151.21[理学—数学]