Just to make sure that I understand correctly, see inline questions below. At 09:20 AM 12/9/2016, Cris Moore wrote:
Did I understand correctly that 2x2 is related to the symmetry of a equilateral triangle in n-space (what is 'n' here?)
yes, where n=2 (n is the size of matrices we're multiplying)
I.e., this is *not* the symmetric group on 3 elements, but the cyclic group of 3 elements, correct?
Did I understand correctly that 3x3 is related to the symmetry of a tetrahedron in n-space (what is 'n' here?)
yes, where n=3, and so on for higher-dimensional simplices - although for n > 2 this construction is not optimal in terms of the tensor rank.
I.e., this is *not* the symmetric group on 4 elements, but the symmetry group of the equilateral tetrahedron in ordinary 3-space? --- Using the same tensor ideas, are there closely related problems that *would* result in the symmetric group of 3 elements; 4 elements? What would such a "generalized matrix multiplication" look like? Any chance that the idea of *solvable groups* comes up in relation to the matrix mult problem? Does this "geometric" line of attack have any elegant treatment of *determinant* computation?