[Haskell-cafe] matrix computations based on the GSL

[Henning Thielemann]

On Wed, 29 Jun 2005, Dan Piponi wrote:

> >On Wed, 29 Jun 2005, Jacques Carette wrote:
>
> >Distinction of row and column vectors is a misconcept
>
> Row and column vectors are sometimes worth distinguishing because they
> can represent entirely different types of object. For example, if a
> column vector represents an element of a vector space V over a field F,
> then row vectors can be used to represent elements of the dual space, V*
> = {f:V->F, f linear}. Quite different objects and in some applications
> it makes sense to distinguish them.

If f is a function
  f :: a -> a
 then, of course, the dual space is again a vector space. But it contains
functionals and they have very different type, namely
  f' :: (a -> a) -> a
 If dual spaces would represent the concept of transposition then the dual
space of the dual space should be original space. It is not, it can even
not be identified in many cases, only if the space is reflexive.
  f'' :: ((a -> a) -> a) -> a
 has certainly a type very different from (a -> a)!