[Haskell-cafe] matrix computations based on the GSL
Keean Schupke
k.schupke at imperial.ac.uk
Fri Jul 8 09:53:34 EDT 2005
Henning Thielemann wrote:
>
>Let me elaborate on that:
> In some cases putting vectors as columns into a matrix then applying a
>matrix operation on this matrix leads to the same like to 'map' a
>matrix-vector operation to a list of vectors. But in other cases (as the
>one above) this is not what you want. I consider it as an incidence not as
>a general principle if this kind of extension works.
>
>Let's consider another example: The basic definition of the Fourier
>transform is for vectors. MatLab wants to make the effect of vector
>operations consistent for row and column vectors, thus
>
>
Okay, this approach is starting to make sense to me... I can see now that
Vectors are a different type of object to Matrices. Vectors represent
points in
N-Space and matrices represent operations on those points (say rotations or
translations)...
But it seems we can represent translations as adding vectors or matrix
operations
(although we need to introduce the 'extra' dimension W... and have an
extra field in vectors
that contains the value '1').
(3D translation)
[x,y,z,1] * [[0,0,0,0],[0,0,0,0],[0,0,0,0],[dx,dy,dz,dw]] =
[x+dx,y+dy,z+dz,1+dw]
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)?
Keean.
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