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Aha, I think I found the ideal place to try and get an answer to my question. Doing multilinear algebra with rank-2 tensors is all fine, but I am unable to get a straight (and simple example) for rank-3 (and hence a generalisation to rank-n).
I have a tensor A_{ijk} where i = 1..10, j=1..5 and k=1..15
and tensor B_{ijk}
Taking a direct step from rank-2 matrices, I want to compute the inner product of Z=AB'
how? and what is the size of Z is it 10x15x10? or...
Actually being even more precise of what I am trying to write out simply is I have A_{ijk} = x_i y_j h_k
and B = A;
So how do I write the dot product Z in terms of x,y and h?
Much appreciated!
David
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