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A proof of Lie’s product formula. (English)
Am. Math. Mon. 121, No. 3, 254-257 (2014).
Summary: For $d \times d$-matrices $A$, $B$ and entire functions $f$, $g$ with $f(0) = g(0) = 1$, we give an elementary proof of the formula $$\lim_{k \to \infty}(f(A/k)g(B/k))^k = \exp(f’(0)A + g’(0)B).$$ For the case $f = g = \exp$, this is Lie’s famous product formula for matrices.
Classification: H65