Matrix Representation of Special Relativity

The possibility to represent Minkowski spacetime vectors with 2x2-matrices is well-known since the 1920ies . It is a consequence of the fact, that the Lorentz-group is homomorphic
to the group of unimodular binary matrices SL(2, C). This matrix representation is mostly used to show, how covariant equations for spinors can be derived.But it is widely ignored, that on the other hand, this also can lead to another description of spacetime itself. There also seems to exist a general consensus, that both representations (matrix form and usual component form) are actually equivalent methods to express the equations of Special Relativity, and consequently the matrix form is used very rarely in publications. One principal reason for this is surely the fact, that conventional component formulas can be formally applied to an arbitrary number of dimensions of the vector space, while the matrix form is only possible for the four-dimensional case. In this article I show, that the presumed equivalence of both forms is not true. Although the equations are isomorphic (otherwise they would be wrong), significantly less prerequisites are needed to derive them for the matrix form. The most important prerequsite is the existence of a metric tensor with the signature (+−− −), that has to be postulated for the vector space, but it is automatically determined for the matrix formalism. In principle, any metric signature would be conceivable for the vector space. Since the metric tensor is at least implicitely contained in every relativistic equation, this statement shows, that the matrix form is superior.