Erdogdu, MelekOzdemir, Mustafa2024-02-232024-02-2320150219-88781793-6977https://doi.org/10.1142/S0219887815500589https://hdl.handle.net/20.500.12452/14181In this paper, Cayley formula is derived for 4 x 4 semi-skew-symmetric real matrices in E-1(4). For this purpose, we use the decomposition of a semi-skew-symmetric matrix A = theta(1)A(1) + theta(2)A(2) by two unique semi-skew-symmetric matrices A(1) and A(2) 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 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).eninfo:eu-repo/semantics/closedAccessMinkowski Space-TimeRotation MatrixCayley FormulaArticle1252-s2.0-84929959889Q3WOS:000355323900007Q410.1142/S0219887815500589