  I compare the matrix representation of the basic statements of Special
Relativity with the conventional vector space representation. It is shown, that
the matrix form reproduces all equations in a very concise and elegant form,
namely: Maxwell equations, Lorentz-force, energy-momentum tensor,
Dirac-equation and Lagrangians. The main thesis is, however, that both forms
are nevertheless not equivalent, but matrix representation is superior and
gives a deeper insight into physical reality, because it is based on much less
assumptions. It allows a better understanding of Minkowski spacetime on the
basis of matrix algebra. An escpecially remarkable result of the consequent
usage of this alge- braic concept is the formulation of Diracs equation in a
novel matrix form. This equation can be generalized to include a new variant of
Yang-Mills gauge fields, which possibly express unified electro-weak
interactions in a new way.
