Gyration Tensor - Diagonalization

Diagonalization

Since the gyration tensor is a symmetric 3x3 matrix, a Cartesian coordinate system can be found in which it is diagonal

$\mathbf{S} = \begin{bmatrix} \lambda_{x}^{2} & 0 & 0 \\ 0 & \lambda_{y}^{2} & 0 \\ 0 & 0 & \lambda_{z}^{2} \end{bmatrix}$

where the axes are chosen such that the diagonal elements are ordered . These diagonal elements are called the principal moments of the gyration tensor.

Read more about this topic: Gyration Tensor