A study of matrix exponential function

Authors:

Carina AGUILAR-CHÁVEZ, Blanca-Esther CARVAJAL-GÁMEZ, José-Luis LÓPEZ-BONILLA

AMS Classification:

11C20, 15A24, 15A90, 53A04, 53B30

Keywords:

exponential function of a matrix, Frenet-Serret formulae, Lorentz equation in Minkowski space

Abstract:

Here we show the importance of a systematic method to generate any integer power of a matrix \underset{\sim}A 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 \exp(\gamma\underset{\sim}A) being  \gamma a scalar. By these reasons, we believe that this work may be of interest for people interested in linear algebra, differential geometry and electrodynamics.

Download paper:

Agui-Carv-Lope-2010

Vol. 5 (13), 2010