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 E 1 4 . 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 A 1 A 2 = 0 , A 1 3 = A 1 and A 2 3 = − A 2 . 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.