[Haskell-cafe] matrix computations based on the GSL
benjamin.franksen at bessy.de
Fri Jul 8 20:54:04 EDT 2005
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?
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