矩阵广义khatri-Rao积的一些性质及不等式  

Some Properties and Inequalities on the Generalized Khatri-Rao Product of Matrices

作　　者：杜鹃[1] 冯思臣[1] 范啸涛[1] 

机构地区：[1]成都理工大学信息管理学院,中国成都610059

出　　处：《湖南师范大学自然科学学报》2009年第3期7-9,22,共4页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(10471112);2008年四川省教育厅自然科学重点资助项目(08ZA114)

摘　　要：在Kronecker积,Hadamared积与Khatri-Rao积的基础上给出了矩阵A,B的广义Khatri-Rao积f(A,B)的定义.并给出了广义Khatri-Rao积f(A,B)的一些普遍性质,得到正定矩阵、半正定矩阵、非负矩阵、Hermite矩阵的广义Khatri-Rao积的特殊性质.推出了广义Khatri-Rao积的共轭转置矩阵运算结果.证明了逆矩阵、平方矩阵的广义Khatri-Rao积的几个重要不等式以及半正定矩阵的广义Khatri-Rao积特征值的性质.Based on the definition of Kronecker product, Hadamard product and Khatri-Rao product, the generalized Khatri-Rao product of matrices A and B, written asf（A ,B）, are defined. Some common properties on the generalized Khatri-Rao product and some special properties on generalized Khatri-Rao product of the specific matrices, such as positive matrix, semi-positive matrix, nonnegative matrix, Hermite matrix are presented. The operation of conjugate transpose on the generalized Khatri-Rao product is deduced out. Moreover, some important inequalities about the generalized Khatri-Rao product of the inverse matrices and square matrices are proved. At last, properties on the eigenvalue of the generalized Khatri-Rao product of the semi-matrices are presented.

关 键 词：矩阵 KHATRI-RAO积 HADAMARD积 KRONECKER积 

分 类 号：O151.21[理学—数学]