How does abstract index notation work? What do the the indices represent? I know the Lorentz transformation tensor in arbitrary direction, so if you want to use a specific tensor in an example, that would be a good one.
In Wald's book he write:
"Thus, the distinction between the index notation and the component notation is
much more one of spirit (i.e., how one thinks of the quantities appearing) than of
substance (i.e., the physical form the equations take)."
So,don't worry it much .