Lie-Trotter Formula for the Hadamard Product

Suppose that A and B are two positive-definite matrices, then, the limit of ( A p /2 B p A 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 ob...

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Bibliographic Details
Published inActa mathematica scientia Vol. 40; no. 3; pp. 659 - 669
Main Authors Wang, Jing, Li, Yonggang, Sun, Huafei
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.05.2020
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
Subjects
Analysis
Mathematics
Mathematics and Statistics
15A42
Lie-Trotter formula
reciprocal Lie-Trotter formula
15A16
47A56
positive-definite matrix
Hadamard product
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Summary:Suppose that A and B are two positive-definite matrices, then, the limit of ( A p /2 B p A 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.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-020-0305-4