These diagonal elements are called the principal moments of the gyration tensor.

The electro-gyration increment of gyration tensor occurred under the action of electric field or/and is written as:

Therefore, the x-y component of the gyration tensor for particles in Cartesian coordinates would be:

Thus, the gyration tensor would be proportional to the inertial tensor if all the particle masses were identical.

As a third method, the radius of gyration can also be computed by summing the principal moments of the gyration tensor.

However, if the principal moments of the two-dimensional gyration tensor are not equal, the column will tend to buckle around the axis with the smaller principal moment.

The theory makes important predictions regarding the change of chain configuration during deformation and relaxation and these are measurable by monitoring the radius of gyration tensor.

As a result, the gyration tensor possessing a symmetry of second-rank axial tensor - is not a subgroup of centrosymmetric media and so the natural optical activity cannot exist in such media.

The key difference is that the particle positions are weighted by mass in the inertia tensor, whereas the gyration tensor depends only on the particle positions; mass plays no role in defining the gyration tensor.