[J3] [EXTERNAL] [BULK] Re: Commutativity of co_reduce

[Clune, Thomas L. (GSFC-6101)]

Hi Malcolm,

I note that although matrix multiply per se is not commutative in general, it is sometimes e.g. when one has matrices that describe rotations in N-space.
I think that this is only true in 2 dimensions.   From Wikipedia (font of all truth, but …)
“The two-dimensional case is the only non-trivial (i.e. not one-dimensional) case where the rotation matrices group is commutative, so that it does not matter in which order multiple rotations are performed. An alternative convention uses rotating axes,[1]<https://en.wikipedia.org/wiki/Rotation_matrix#cite_note-1> and the above matrices also represent a rotation of the axes clockwise through an angle θ.”

Other properties of the result are also preserved with commutation, even when the exact value is not. So there can be value even in operations that appear to be non-commutative.
Strong agreement on this.   But I am left wondering if a similar statement can be made for associativity?


  *   Tom


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://mailman.j3-fortran.org/pipermail/j3/attachments/20241025/f315f0c1/attachment.htm>