[boost] outer, cross product operand types (was Re: [rfc] A light weight statically typed matrix template class (again?)

From: Larry Evans (cppljevans_at_[hidden])
Date: 2007-12-12 15:23:58

On 12/12/07 11:08, Dave Steffen wrote:
> On Monday 10 December 2007, Andreas Harnack wrote:
[snip]
>> As far as I'm aware there's only one product to matrices; we're
>> not talking about vectors here ;-). Of course, you can use row-
>> or column-matrices to represent vectors, in which case the
>> result (i.e. scalar or matrix) depends on the order of operands.
> 
>   You're kidding, right?  There are many ways to multiply two matrices
>   together.  I listed three above.  Cross products are a fourth.
>   The correct interface depends *heavily* on the intended uses.
> 
I also thought outer and cross product dealt with vectors.
The following page on outer product:

http://documents.wolfram.com/mathematica/Built-inFunctions/AdvancedDocumentation/LinearAlgebra/LinearAlgebraInMathematica/MatrixAndTensorOperations/MatrixMultiplication/AdvancedDocumentationLinearAlgebra1.6.0.html

seems to support that conclusion about outer product, and the following
on cross product:

http://planetmath.org/encyclopedia/CrossProduct.html

also supports that interpretation for cross product.  I guess
we're both (i.e. me and Andreas) thinking too narrowly.  Could
you provide some web page supporting your interpretation that
outer and cross args are matrices instead of vectors?

OOPS, wait.  Looking at:

http://planetmath.org/encyclopedia/OuterMultiplication.html

maybe supports your interpretation, although I can't yet
understand all the notation.

Anyway, even if I and Andreas are thinking too narrowly,
the first two web pages referenced suggest that thinking
is understandable and maybe common for those not real
familiar with the field.

-regards,
Larry