Lie-Trotter Formula for the Hadamard Product

• Published in: Acta mathematica scientia Vol. 40; no. 3; pp. 659 - 669
• Main Authors: Wang, Jing, Li, Yonggang, Sun, Huafei
• Format: Journal Article
• Language: English
• 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

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...