[l33t2328]

I think it’s a little funny you said that

>[the explanation in the OP] will make sense to physicist, but no sense to most everyone else, including mathematicians

And then went on to describe tensors in a way that is unfriendly to non mathematicians by saying

> tensors are a sort of universal objects representing multi linear maps: bilinear maps V x W -> R correspond canonically one-to-one to regular linear maps V (x) W -> R, where V (x) W is a vector space called tensor product of V and W, and tensors are simply vectors in this tensor product space.