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Discussion: new operators for numerical computation

Huaiyu Zhu hzhu at knowledgetrack.com
Fri Jul 21 19:44:07 EDT 2000 
On Thu, 20 Jul 2000 19:32:15 +0100, Robin Becker
<robin at jessikat.fsnet.co.uk> wrote: 
>In article <slrn8nefig.rb.hzhu at localhost.localdomain>, Huaiyu Zhu
><hzhu at localhost.localdomain> writes
>>
>>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
>
>I'd be interested in how you define either Kron and * to achieve the
>result you claim without modifying the p x r matrix B; after all it
>cannot involve sums of elements of B so * isn't the matrix multiply. I
>could use an element wise multiply, but only if I use the end desired
>shape as the second element.

Oops.  You are right.   B has to change as well.  It is 

kron(A,B) == kron(A,I1) * kron(I2,B)

where I1, I2 are identity matrices which, in fact, depend on the dimensions
of the other.  In matlab notation I1=eye(size(B,1)), I2=eye(size(A,2)).

So it involes expanding the dimension of both operator according to the
dimension of the other operator and then compose them. 

Huaiyu
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