Lie-Trotter Formula for the Hadamard Product - Wang, Jing; Li, Yonggang; Sun, Huafei (Acta mathematica scientia, 2020)
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.