Abstract
Suppose that A and B are two positive-definite matrices, then, the limit of (Ap/2BpAp/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 (Ap * Bp)1/p as p tends to 0. Furthermore, the existence of the limit of (Ap * Bp)1/p as p tends to +∞ is proved.
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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).
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Wang, J., Li, Y. & Sun, H. Lie-Trotter Formula for the Hadamard Product. Acta Math Sci 40, 659–669 (2020). https://doi.org/10.1007/s10473-020-0305-4
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DOI: https://doi.org/10.1007/s10473-020-0305-4