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

页码：254 / 257

页数：4

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