一些包含Khatri-Rao积的矩阵不等式  

Some Matrix Inequalities Involving the Khatri-Rao Product

作　　者：任林源[1] 

机构地区：[1]西安工业大学数理系,陕西西安710032

出　　处：《延安大学学报（自然科学版）》2011年第1期1-3,9,共4页Journal of Yan'an University：Natural Science Edition

基　　金：陕西省教育厅科研计划项目(09JK494);校长科研基金项目(XAGDXJJ0930)

摘　　要：利用Styan和Liu的相关结果,主要研究了分块和非分块矩阵的Khatri-Rao积,Khatri-Rao和与Hadamard积的矩阵不等式,得到一些半正定矩阵和非奇异Herm itian矩阵含有Ktracy-Rao积等的矩阵不等式。所得含有Khatri-Rao积的矩阵不等式可用于其它矩阵不等式方向的研究。Using the results provided by Styan and S.Liu,this paper is concerned with the inequality of matrix product for portioned and non-partitioned matrices,which involving the Khatri-Rao product,Khatri-Rao sum,and Hadamard product.Several product inequalities are obtained in the positive semi-definte matrix and in the non-singular Hermitian matrix case.It is easy to apply the result of inequalities involving the Khatr-Rao prouduct to the research in other fields.

关 键 词：矩阵不等式 半正定矩阵 HADAMARD积 KHATRI-RAO积 Tracy-Singh积 KRONECKER积 

分 类 号：O151.21[理学—数学]