LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT

doi:10.1007/s10473-020-0305-4

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 659-669.doi: 10.1007/s10473-020-0305-4

LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT

王静¹, 李永刚², 孙华飞³

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

收稿日期:2018-10-24 修回日期:2019-05-17 出版日期:2020-06-25 发布日期:2020-07-17
通讯作者: Jing WANG E-mail:wangjingzzumath@163.com
作者简介:Yonggang LI,E-mail:liyonggang914@126.com;Huafei SUN,E-mail:huafeisun@bit.edu.cn
基金资助:
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).

LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT

Jing WANG¹, Yonggang LI², Huafei SUN³

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

Received:2018-10-24 Revised:2019-05-17 Online:2020-06-25 Published:2020-07-17
Contact: Jing WANG E-mail:wangjingzzumath@163.com
Supported by:
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/Abstract

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

Abstract: 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.

Key words: Lie-Trotter formula, reciprocal Lie-Trotter formula, Hadamard product, positive-definite matrix

中图分类号:

15A42

王静, 李永刚, 孙华飞. LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT[J]. 数学物理学报(英文版), 2020, 40(3): 659-669.

Jing WANG, Yonggang LI, Huafei SUN. LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT[J]. Acta mathematica scientia,Series B, 2020, 40(3): 659-669.

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LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT

LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT

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