- #1
Paalfaal
- 13
- 0
I'm trying to prove eA eB = eA + B using the power series expansion eXt = [itex]\sum_{n=0}^{\infty}[/itex]Xntn/n!
and so
eA eB = [itex]\sum_{n=0}^{\infty}[/itex]An/n! [itex]\sum_{n=0}^{\infty}[/itex]Bn/n!
I think the binomial theorem is the way to go: (x + y)n = [itex]\displaystyle \binom{n}{k}[/itex] xn - k yk = [itex]\displaystyle \binom{n}{k}[/itex] yn - k xk, ie. it's only true for AB = BA.
I'm really bad at manipulating series and matrices. Could I please get some hints?
and so
eA eB = [itex]\sum_{n=0}^{\infty}[/itex]An/n! [itex]\sum_{n=0}^{\infty}[/itex]Bn/n!
I think the binomial theorem is the way to go: (x + y)n = [itex]\displaystyle \binom{n}{k}[/itex] xn - k yk = [itex]\displaystyle \binom{n}{k}[/itex] yn - k xk, ie. it's only true for AB = BA.
I'm really bad at manipulating series and matrices. Could I please get some hints?
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