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The notation is very simple: you write tensor expressions with indices, and repeated indices are implicitly summed over. For example, matrix multiply: A_ij
by jules 9y ago
The 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.