Yes, the tensors here are meant to be used as in physics textbooks. Physicists try to avoid to use components explicitly, because otherwise there would often be no space on the book papers. All the reasoning is kept on the index manipulation and contraction logic, as well as commutative properties of tensors. In any way, they still are a generalization of both matrices and linear operators. Matrix algebra, vector calculus are just special cases of tensor algebra and calculus.

I added this example because there was a bug report two months ago. In the discussion it came out that it is not clear how to use components data in tensors from the current documentation.