What exactly is a tensor in theano?

Question

What exactly is a Tensor in Theano, and what is the precise connection with Tensors as they are typically understood in Physics or Math?

I went through the Theano at Glance and the Basic Tensor functionality, but I could not find a clear connection.

Answer 1

There is a good breakdown of different physics/math ways to think of tensor in Jim Belk's answer to a question on math.stackexchange. After looking over the documentation on tensor and the various operations Theano provides I'd say Theano's notion of tensor corresponds to the first way of thinking of tensor. In Jim's words:

Tensors are sometimes defined as multidimensional arrays, in the same way that a matrix is a two-dimensional array. From this point of view, a matrix is certainly a special case of a tensor.

In any case, I don't see anything myself in the docs indicating that Theano's tensor implementation knows about global properties of manifolds or tensor products in linear algebra beyond defining dot-products and the like. This would indicate Theano is taking a local point of view in it's implementation as opposed to the global.