If one thinks of vectors as the matrix of some linear map over the scalars (and similarly covectors as linear maps to the scalars), and assuming the usual compo

If one thinks of vectors as the matrix of some linear map over the scalars (and similarly covectors as linear maps to the scalars), and assuming the usual composition order of maps then it seems there is no choice as to the column/row representation: vectors have to be (n x 1) and covectors have to be (1 x n) This doesn't say anything regarding their practical storage, but at least conceptually vectors/covectors are a bit more than just a collection of numbers. This distinction is pretty useful in practice when encoded in types to avoid implicitly mixing things that are conceptually different.