[Haskell-cafe] vector-space and standard API for vectors

[Daniel Fischer]

On Saturday 23 October 2010 22:53:32, Alexey Khudyakov wrote:
> > type family Scalar :: * -> *
> >
> > class Additive v => LeftModule v where
> >   (*^) :: Scalar v -> v -> v
> >
> > class Additive v => RightModule v where
> >   (^*) :: v -> Scalar v -> v
>
> Could you give some example of data type for which (*^) ≠ flip (^*)?
> I couldn't imagine one.

Take any noncommutative ring R (quaternions for example) and consider the 
space R^n as a) a left R-module and b) a right R-module.