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
matrix
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. John Phillips
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