[Haskell-cafe] matrix computations based on the GSL

[karczma at info.unicaen.fr]

Jacques Carette writes: 

> Henning Thielemann wrote:

>> I don't see the problem. There are three very different kinds of
>> multiplication, they should also have their own signs: Scalar product,
>> matrix-vector multiplication, matrix-matrix multiplication.
>>  

> You see 3 concepts, I see one: multiplication.  Abstract Algebra is the 
> branch of mathematics where you want to abstract out the *unimportant* 
> details.  Much progress was made in the late 1800's when this was 
> discovered by mathematicians ;-).

One of the things I appreciate and I hate simultaneously in your postings
is that you are so categorical. 

This time you will *not* convince me that there is "one concept: multipli-
cation", moreover "abstracted over unimportant details". 

If matrices represent operators, their multiplication is a *group*
operation, the op. composition. Acting of a matrix on a vector is not. 

"Multiplication" of two vectors giving a scalar (their contration) is
yet another beast. I believe that some progress has been done in math,
when people discovered that mixing-up things is not necessarily a good
thing, and different entities should be treated differently. 

Jerzy Karczmarczuk