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.
Geometry Tensors
Projection Tensor
Pe = 


= 
cos^{2}α 
sin α cos α 
sin α cos α 
sin^{2} α 

Rotation Tensor
Reflection Tensor
Mechanics Tensors
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.
I = 
∫ r^{2} dm = 
Ix 
Pxy 
Pxz 
Pxy 
Iy 
Pyz 
Pxz 
Pyz 
Iz 

The Inertia Tensor in 'n' dimensions is discussed on this page.
Stress Tensor
Strain Tensor
Elastic Tensor