LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT  

作　　者：Jing WANG Yonggang LI Huafei SUN 王静;李永刚;孙华飞(School of Information,Beijing Wuzi University,Beijing 101149,China;College of Science,Zhengzhou University of Aeronautics,Zhengzhou 450015,China;School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China;Beijing Key Laboratory on MCAACI,Beijing 100081,China)

机构地区：[1]School of Information,Beijing Wuzi University,Beijing 101149,China [2]College of Science,Zhengzhou University of Aeronautics,Zhengzhou 450015,China [3]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China [4]Beijing Key Laboratory on MCAACI,Beijing 100081,China

出　　处：《Acta Mathematica Scientia》2020年第3期659-669,共11页数学物理学报（B辑英文版）

基　　金：H.Sun is supported by NSFC(61179031);J.Wang is supported by General Project of Science and Technology Plan of Beijing Municipal Education Commission(KM202010037003).

摘　　要：Suppose that A and B are two positive-definite matrices,then,the limit of(A^p/2B^pA^p/2)1/p as p tends to 0 can be obtained by the well known Lie-Trotter formula.In this article,we generalize the usual product of matrices to the Hadamard product denoted as*which is commutative,and obtain the explicit formula of the limit(A^p*B^p)^1/p as p tends to 0.Furthermore,the existence of the limit of(A^p*B^p)^1/p as p tends to+∞is proved.

关 键 词：Lie-Trotter formula reciprocal Lie-Trotter formula Hadamard product positive-definite matrix 

分 类 号：O151.21[理学—数学]