On Friday 08 July 2005 17:46, Henning Thielemann wrote:
Vectors can be used and abused for many things but an object which can be called a vector (because of its ability of to be added and to be scaled) is not a linear operator itself and does not naturally represent one.
At least for finite dimensional spaces (and these are the only ones under consideration here, right?) scalar multiplication is a very nice and natural way to view a vector as a linear operation (into the scalar field). I know, in linear algebra the told us all that this corespondence is not a 'natural' or 'canonic' one because it depends on a chosen basis. Well, well. For practical purposes of programming, we always use the 'canonic base' right? So if the base is canonic, then so is the correspondence between vector space and its dual. On a different not, one could argue that a 1xn matrix M is indeed a vector of dimension n, an then M' = M^T is a nx1 matrix, that is also a vector of dimension n, but this is the same vector as the non-transposed version. Now, the two things (M and M') are the same, if viewed as a vector, but not the same if viewed as a matrix. Can we express this in Haskell? Ben