Discussion: new operators for numerical computation

[Huaiyu Zhu]

On Thu, 20 Jul 2000 17:37:12 +0200, Gregory Lielens <gregory.lielens at fft.be>
wrote: 
>
>Are you talking of matrices, or Nd arrays? I am only aware of one kind
>of matrix multiply, defined as
>
[snip]
>
>For Nd arrays, there is indeed more possibilities, and I fear adressing
>all of them could be too much to ask to "simple" infix operators....
[snip]

Infix notations are suitable and convenient for linear algebra.  But for
multilinear algebra there is no avoidance of dummy indices, like

contract(A,(1,3),B,(5,2))

which contracts the correspoding indices of A with those of B. This is why
in theretical physics and differential geometry the Einstein notation is
almost universally used and one rarely sees matrix notation.

When it comes to number crunching, however, matrix is far more common. Imho,
consideration of tensor and multilinear algebra is somewhat off-topic.

>imho Division (right and left) belongs to pure matrices, and can not
>really be generalized
>I feel that way because I am not aware of a well defined inverse for a
>Nd array ...(should someone be interrested in this I could post a
>discussion I had with Travis Oliphant, from NumPy group)

That's another reason we should concentrate in linear algebra only.

[Digression: multilinear algebra is in fact a special case of highly
singular linear algbra, albeit in higher dimensional space.  See kron(a,b)]

-- 
Huaiyu Zhu                       hzhu at users.sourceforge.net
Matrix for Python Project        http://MatPy.sourceforge.net