# [Haskell-cafe] matrix computations based on the GSL

Henning Thielemann lemming at henning-thielemann.de
Fri Jul 8 11:46:40 EDT 2005

```On Fri, 8 Jul 2005, Keean Schupke wrote:

> Henning Thielemann wrote:
>
> >Do you mean
> > [x,y,z,1] * [[1,0,0,0],[0,1,0,0],[0,0,1,0],[dx,dy,dz,dw+1]]
> >?
> >
> Erm, yes thats what I meant ... but you obviously got the point.
>
> >>but how is this different from adding vectors? If we allow vector
> >>addition then we no longer have the nice separation between values and
> >>linear operators, as a value can also be a linear operator (a
> >>translation)?
> >
> >???
>
> Well if a vector can be a linear-operator, then surely it _is_ a matrix!

In general a vector need not to be a linear operator. You talked about
vector translation, translation is not a linear operator. You gave some
process to map the problem to somewhere, where it becomes a linear
operator. Other people said that the scalar product with a fixed vector is
a linear operator. That's true. Now what is a natural interpretation of a
vector as linear operator? The scalar product or the translation? 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.

```