A $2d$ system consists of $N$ identical cells arranged linearly in series. The transfer matrix of a single cell is an unitary Hermitian $2$x$2$ matrix with eigenvalues $\exp(±i\theta)$.

I need to use Sylvester's theorem to deduce the values of $\theta$ , for which the transmission coefficient through the system is equal to $1$. Can anybody help me on how to apply it, any formulas? My professor gave us this problem, but he never mentioned Sylvester's theorem. I searched online but I got confused.


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