3 ms·
I don't find it very accessible, myself - but I'm not a physicist, so the materials using or about that notation aren't aimed at me. The only tensor notation I
by jph00 9y ago
I don't find it very accessible, myself - but I'm not a physicist, so the materials using or about that notation aren't aimed at me.
The only tensor notation I've been happy with is that used in J (http://www.jsoftware.com http://www.jsoftware.com), which is simple, flexible, and concise.
There's also some nice-enough modern notation used in this excellent review: http://www.cs.cmu.edu/~christos/courses/826-resources/PAPERS+BOOK/Kolda-Bader-SAND2007-6702.pdf http://www.cs.cmu.edu/~christos/courses/826-resources/PAPERS...
- deleted 9y ago[deleted]
- jules 9y agoThe notation is very simple: you write tensor expressions with indices, and repeated indices are implicitly summed over. For example, matrix multiply: A_ij = B_ik C_kj Differentiating this with respect to variable l: ∂_l A_ij = ∂_l (B_ik C_kj) = (∂_l B_ik) C_kj + B_ik (∂_l C_kj) By writing out indices you can just use the rules for scalar derivatives.
- jph00 9y agoOh in that case I'm just confused - that's what I know as Einstein notation. Modern physics papers seemed to use much more complex notation, but I probably just misunderstood. If we're talking about Einstein notation, then I'm a fan - `np.einsum()` is often a great way to create fast tensor computations with minimal code.