Abstract
In this paper, Cayley formula is derived for 4 × 4 semi-skew-symmetric real matrices in [Formula: see text]. For this purpose, we use the decomposition of a semi-skew-symmetric matrix A = θ1A1+ θ2A2by two unique semi-skew-symmetric matrices A1and A2satisfying the properties [Formula: see text] and [Formula: see text] Then, we find Lorentzian rotation matrices with semi-skew-symmetric matrices by Cayley formula. Furthermore, we give a way to find the semi-skew-symmetric matrix A for a given Lorentzian rotation matrix R such that R = Cay (A).
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