- #1
mjordan2nd
- 177
- 1
Homework Statement
I am asked to prove that [itex]e^{iB}[/itex] is unitary if B is a self-adjoint matrix.
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.