I'm getting a bit stuck on what this is telling me:

Firstly, is this restricted to since it has 9 cartesian components? In , would it have cartesian components?Consider a tensor of order 2. Define the 9 cartesian components of T by .

Secondly, is it true that would be the different entries in a matrix representing T?

Finally, what is ? I thought that T was a linear map (well, a tensor) so shouldn't T be defined on how it acts upon a vector, or is this notation that I haven't encountered before?

Thanks for any help!