A Proof of Lie's Product Formula

被引：5
|
作者：
Herzog, Gerd [1 ]
机构：
[1] Karlsruher Inst Technol, Inst Anal, D-76128 Karlsruhe, Germany
来源：
AMERICAN MATHEMATICAL MONTHLY | 2014年 / 121卷 / 03期
关键词：
D O I：
10.4169/amer.math.monthly.121.03.254
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For d x d-matrices A, B and entire functions f, g with f(0) = g(0) = 1, we give an elementary proof of the formula lim(k ->infinity) (f (A/k)g(B/k))(k) = exp(f'(0) A + g' (0) B). For the case f = g = exp, this is Lie's famous product formula for matrices.
引用
收藏
页码：254 / 257
页数：4
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