A 1D list of numbers is not necessarily a "vector" in the Differential Geometry sense. The definition of a vector or tensor is based on how it transforms as the co-ordinate system transforms. See e.g. http://en.wikipedia.org/wiki/Covariance_and_contravariance_o...
One weird consequence of this is that if A and B are vectors, the cross product (AxB) is NOT a vector in the tensorial sense. [Aside: Cross products are really weird since they are defined in the familiar way 3 and 7 dimensions only! (see http://math.stackexchange.com/questions/185991/is-the-vector...]
One weird consequence of this is that if A and B are vectors, the cross product (AxB) is NOT a vector in the tensorial sense. [Aside: Cross products are really weird since they are defined in the familiar way 3 and 7 dimensions only! (see http://math.stackexchange.com/questions/185991/is-the-vector...]