) is a vector. In general, the operation of differentiation with respect to time does not alter the tensor character. Since
is an invariant (tensor of rank 0),
) is a vector, or tensor of rank 1 (by the theorem of the multiplication of tensors). If the force (
) has a vector character, the same holds for the difference (
. These equations of motion are therefore valid in every other system of Cartesian co-ordinates in the space of reference. In the case where the forces are conservative we can easily recognize the vector character of (