In order to be a tensor, a quantity needs to be a linear function. It also needs to change, according to certain rules, in response to a change of frame.
||sin α cos α
|sin α cos α
Inertial Moment Tensor
This relates the torque bivector to the angular acceleration bivector of a solid body. This is a property of the solid body. In three dimensions it is defined by a 3×3 matrix, the components of it depends on its shape and in particular its mass distribution, however the way that these components vary with a change in reference frame is a tensor property.
||∫ r2 dm =
The Inertia Tensor in 'n' dimensions is discussed on this page.