Relativistic motion of classical charged particles in a uniform electromagnetic field

Here we show the importance of a systematic method to generate any integer power of a matrix in 2, 3 and 4 dimensions. This is motivated by the integration of Frenet–Serret formulae for the case of constant curvatures, and by the relativistic motion of a point charge into a homogeneous electromagnetic field, because in such situations it is necessary to calculate being a scalar. By these reasons, we believe that this work can be useful for people interested in linear algebra, differential geometry and electrodynamics.