Matrix solution for the inverse problem of classical dynamics of a particle

We solve the inverse problem corresponding to the fundamental problem of the classical dynamics of a material particle through a matrix treatment: assuming knowing the mass and the position (the trajectory, in relation to an inertial reference) of a particle at all times, we impose that this corresponds to the eigenvector of a “position matrix". Subsequent development leads to a “force matrix", which has the resultant force on the particle as its eigenvector. We identified some limitations of this matrix treatment.