[Haskell-cafe] matrix computations based on the GSL
k.schupke at imperial.ac.uk
Fri Jul 8 12:16:29 EDT 2005
Henning Thielemann wrote:
>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.
So the linear operator is translation (ie: + v)... effectively 'plus'
viewed as a function which takes a vector and returns a matrix (operator)
(+) :: Vector -> Matrix
Which could also be called 'translate'. So 'translate' takes a vector
a linear-operator which can be applied to a vector:
mapply (translate vector1) vector2
So I guess I could now ask, why allow vector addition at all?
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