I am reading Zee's QFT in a nutshell, 2nd ed. On pg. 97 below eq. 14 he writes:
$$ S \gamma^{\lambda } S^{-1} = \omega_{\,\, \mu }^{\lambda } \gamma ^{\mu }+\gamma ^{\lambda }. $$
Building up a finite Lorentz transformation by compounding infinitesimal transformations (just as in the standard discussion of the rotation group in quantum mechanics), we have $$S \gamma ^{\lambda } S^{-1}= \Lambda ^{\lambda }_{\,\,\mu } \gamma ^{\mu}.$$
I am having trouble seeing how this second equation follows from the first. I would very much appreciate some help on what are the in between steps.