## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

# A Proof of Lie’s Product Formula

Gerd Herzog
The American Mathematical Monthly
Vol. 121, No. 3 (March 2014), pp. 254-257
DOI: 10.4169/amer.math.monthly.121.03.254
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.03.254
Page Count: 4
Item Type
Article
References
Preview not available

## Abstract

Abstract For d × d-matrices A, B and entire functions f, g with f(0) = g(0) = 1, we give an elementary proof of the formula \documentclass{article} \pagestyle{empty}\begin{document} $$\lim_{k \to \infty} (f(A/k) g(B/k))^k = \exp(f'(0)A+g'(0)B).$$ \end{document} For the case f = g = exp, this is Lie’s famous product formula for matrices.