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lang-py
ij,jkcould work by itself (without the arrows) to form the matrix multiplication. But it seems like for clarity it's best to put the arrows and then the output dimensions. It's in the blog post.Ais of length 3, the same as the length of the columns inB(whereas rows ofBhave length 4 and cannot be multiplied element-wise byA).->affects the semantics: "In implicit mode, the chosen subscripts are important since the axes of the output are reordered alphabetically. This means thatnp.einsum('ij', a)doesn’t affect a 2D array, whilenp.einsum('ji', a)takes its transpose."