From: John Phillips (phillips_at_[hidden])
Date: 2006-06-12 11:04:51
Leland Brown wrote:
> Janek Kozicki <janek_listy <at> wp.pl> writes:
>>Leland Brown said: (by the date of Fri, 9 Jun 2006 04:31:28 +0000 (UTC))
>>>Actually, yes! In fact, I played around quite a bit with allowing my
>>>elements to be matrices themselves, and even implemented some of it.
>>wouldn't it be tensors, then?
> They act like partitioned matrices. The elements are submatrices of the larger
> matrix. The same results can be obtained by putting all the individual scalar
> elements into one big matrix, so there's not really any new functionality with
> this, just notational convenience for some problems.
> Tensors are a bit over my head, but I assume their semantics are different than
> simply a partitioned matrix. I don't think what I implemented would produce
> tensor algebra.
> -- Leland
What it means to be a tensor is defined in terms of transformation
properties. If the object transforms the proper way, it is a tensor, if
not, it is not. Matrices may or may not be tensors, and certainly, many
types of tensors can't be represented as simple matrices (since they can
be more than 2 dimensional).
The matrix elements are other matrices approach is something I've
only used in the way Leland describes it. It is effectively a
partitioning, and I have only used it in cases where it helps organize
what I'm looking at. Maybe others have done other things with it.
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