With the relation of Olinde Rodrigues-Cartan is obtained an expression for the Lorentz matrix, and it is transformed to a better form for the Newman-Penrose formalism, thus it is possible to realize rotations of the null tetrad of NP.
The Bulletin of Society for Mathematical Services and Standards (Volume 11)
I. Guerrero-Moreno et al., "Rotations in Minkowski Spacetime", The Bulletin of Society for Mathematical Services and Standards, Vol. 11, pp. 23-25, 2014