On the Rotation Matrix in Minkowski Space-Time

In this paper, a Rodrigues-like formula is derived for 4 × 4 semi skew-symmetric real matrices in E14. For this purpose, we use the decomposition of a semi skew-symmetric matrix A = θ1A1 + θ2A2 by two unique semi skew-symmetric matrices A1 and A2 satisfying the properties A1A2=0,A13=A1 and A23=−A2. Then, we find Lorentzian rotation matrices with semi skew-symmetric matrices by Rodrigues-like formula. Furthermore, we give a way to find the semi skew-symmetric matrix A for a given Lorentzian rotation matrix R such that R = eA.