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.
Jing WANG
,
Yonggang LI
,
Huafei SUN
. LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT[J]. Acta mathematica scientia, Series B, 2020
, 40(3)
: 659
-669
.
DOI: 10.1007/s10473-020-0305-4
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