Discussion: new operators for numerical computation

[Huaiyu Zhu]

On Thu, 20 Jul 2000 17:06:03 +0100, Robin Becker
<robin at jessikat.fsnet.co.uk> wrote: 
>
>the kronecker product is also called the matrix direct product
>
>
>A ox B = [a11 B a12 B]
>         [a12 B a22 B]
>
>seems to me to be like a tensor outer product; but I ain't no
>mathematician ;)

In matlab/octave, this is called kron(A,B).  I don't think it deserves an
infix operators, because it is just a special case of matrix multiplication.
You can define a sparse matrix Kron(A) so that

kron(A,B) == Kron(A)*B

For such specializations it is best to explicitly spell out the names of
operators.  This is also true of unitary functions.  + - have symbols but
sin, cos, ... do not.

>the lie product (or bracket) has applications in sensitivity analysis
>and other more exotic stuff in differential geometry
>
>[A,B] = AB - BA

def lie(a,b): return a*b-b*a

On the other hand, the difference between elementwise and matrix operators
are much more fundamental.  They result from the different views of vectors,
either as a simple collection of numbers, or as a point in a linear space
that happens to be represent by an array of numbers.

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