(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am asked to prove that [itex]e^{iB}[/itex] is unitary if B is a self-adjoint matrix.

3. The attempt at a solution

In order to prove this I am attempting to show [itex]e^{iB} \widetilde{e^{iB}} = 1[/itex]. Using the assumption that B is self-adjoint I have been able to show that

[tex]

e^{iB} \widetilde{e^{iB}} = \sum_{n=0}^{\infty} \sum_{m=0}^{\infty} \frac{(-1)^m i^{m+n} B^{m+n}}{m!n!}.

[/tex]

I have looked at the first few powers of B and shown that the coefficients go to 0. I expect that this is the case in general for m+n>0, however I am having difficulty proving this (for m,n=0 the term is 1). Can anyone point me in the right direction? Thanks.

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# Homework Help: Need help proving that an infinite double sum is 1

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