I have 2 basic questions: 1. Since a type (m,n) tensor can be created by component by component multiplication of m contravariant and n covariant vectors, does this mean an (m,n) tensor can always be decomposed into m contravariant and n covariant tensors? Uniquely? 2. Since a tensor in GR , or perhaps even more generally, is invariant with a change in coordinate system, can the vectors used to create it by component by component multiplication each be of different coordinate systems? And, if so, would the coordinate transformation equations for the multi-coordinate system tensor be the same form as the contravariant and covariant transformation equations for moving a tensor from one coordinate system to another?