Norbert Nemec wrote:
> Hi there,
> 
> thinking further about the clash of + as addition and concatenation, I
> had an even better idea:
> 
> How about generally introducing [+], [*] and so on as elementwise
> operations? This avoids the clash with the double meaning of + and *,
> adds to the readability, since you see whether an operation handles
> objects or collections offers a number of cool possibilities:
> 
>     A = [1,2]
>     B = [3,4]
> =>
>     A + B == [1,2,3,4]  # as before
>     A [+] B == [4,6]
>     A [*] B == [3,8]
> 
> If one of the arguments is not a list, it is distributed:
> 
>     A [+] 1 == [2,3]

yeah apparently this was proposed for Python at one time too:
http://www.python.org/peps/pep-0225.html
except the favored syntax was A ~+ B instead of A [+] B.  Actually
A .+ B was his first choice, but probably the parser wouldn't allow it 
because uglies like this are allowed: "1 . ToString()"
There are also some interesting proposals for Perl:
http://dev.perl.org/perl6/rfc/207.html  like A[|i] + B[|i]

For now I'd just recommend a .NET math lib like dnAnalytics:
http://www.dnanalytics.net/  See its DoubleVector and DoubleMatrix 
classes.  A+B is element-wise for its vectors, but you can still do 
things like slicing.  Remember to turn rawArrayIndexing on too if needed.

Some related info:

You can define your own custom infix operators in languages like Nemerle 
or LiveLogix's Logix using macros.

There doesn't appear to be a standard computer math syntax for things 
like dot products, cross products, etc.:
java expression parser example:
http://www.singsurf.org/djep/html/djep/VectorJep.html#VEC
scilab example:
http://www.engineering.usu.edu/cee/faculty/gurro/Software_Calculators/Scilab_Docs/Scilab_scripts/Vectors_Script.sce

Related also is the JScience proposal for adding scientific unit classes 
and conversions: http://www.jscience.org/  They wished to extend java's 
syntax too to make it easier to use units, but that's not going to happen.