On the application geometric algebra in the lorentz transformation

The aim of this paper is to provide understanding of the relation between the application of Geometric Algebra in the Lorentz Transfor-mation and the conventional coordinate-based approach. The relation between the variables used in both approaches will be assessed and the relative eciency of the Geometric Algebra will be established. The general Lorentz Transformation will be subdivided into a rotation and a boost transformation. This opens the way to write the exponent no-tation of the Geometric Algebra product as a Taylor series to discover the sine-cosine or hyperbolic sine-cosine alternative notation, which can successively be used to nd the old notation. The power of the Geometric Algebra, it will be assessed, lies in the fact that it can solve the Lorentz Transformation without choosing any coordinate system.