1. When can I contract a tensor? Is that an option to contract for example a (1, 1) tensor to a real number or has that to happen for some tensors and for some don’t? Or put differently, when am I allowed to sum over one upper and one lower index? 2. I read in Schutz “Geometrical methods..” that a general (2, 0) tensor cannot be expressed as a simple outer product of two vectors. He says that’s because in n dimensions a (2, 0) tensor has n^2 independent components, while two vectors have between them only 2n components and in general this is inadequate. I don’t quite understand. Is the independence of components here crucial? And does that really mean that tensors in general can not be constructed by forming tensor products of vectors and covectors? I thought that was kind of the definition of tensors? As always I hope my questions make sense and thanks for replies.