Is Mass a Tensor?

Typically, mass is a scalar. But when looking at neutrino masses (or for that matter, quark masses), there is a matrix that corresponds to how masses enter into the Lagrangian. In that sitation, it could be appropriate to talk about a mass tensor. It turns out that the matrix is not diagonal which underlies the reason why different neutrino types can convert into each other (neutrino oscillations).

There is an inertia tensor ( I ) associated with a rigid distributed mass that relates the angular momentum vector J to the angular velocity vector W. J=I*W, where * is the matrix multiplication operator. It's analogous to momentum =mass X velocity for lineear motion. Is that what you're thinking of?

This means that mass is a linear quanity. Linear meaning it is only in in one direction down. I used to think of a string holding a mass in tension like I would imagine a "tensor". The string would be the opposing force to the force of gravity or the mass of the object.