Gyration tensor

In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles

where ${\displaystyle r_{m}^{(i)}}$ is the ${\displaystyle \mathrm {m^{th}} }$ Cartesian coordinate of the position vector ${\displaystyle \mathbf {r} ^{(i)}}$ of the ${\displaystyle \mathrm {i^{th}} }$ particle. The origin of the coordinate system has been chosen such that

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