Tensors
Hi, I've decided to learn GR recently since it's like the "sexy" side of physics. But I'm getting stuck with the tensors notations already. Maybe my math background is just not sufficient enough to do GR.
In general, how do I show that an object is tensorial; for example, objects like TabTba or Tab  Tba ( for partial derivatives,  for covariant derivatives and Ta or Tb are just the covariant vector components.)
Also, in general, how do I solve for the roots of a determinant equation that invovles tensors? For example, det(k Amn  Bmn) = 0 where Amn and Bmn are covariant tensor components and I suppose k is the eigenvalue(or maybe not...?). Is this the same as in linear algebra where we just solve for all the possible eigenvalues? But I'm confused with the covariant tensor components, can I just treat them as entries of a matrix? Thanks.
