3-dimensional Lorentzian space Cayley formula, Euler parameters

In this study, Lorentzian matrix ( L -matrices) using the product of 3-dimensional Lorentz space, Cayley formula and the rotation axis spacelike and timelike vector L -ortogonal matrix Euler parameters were obtained. The Cayley formula is a method of finding the orthogonal matrix corresponding to a rotation about a given axis. Since the use of the split quaternion multiplication-matrix form is a convenience, L -the Euler parameters of the orthogonal matrix are used in a split quaternion, the L -version is given by the split quaternion equation.