Haha. Thanks.
I agree that the description is not as clear as it could be, but maybe it’s more the shaping that isn’t clear rather than the mathematical bits.

for each subtensor v over dimension dim of input.

Maybe it becomes clearer when you add the shape information: For a tensor of sizes (n_0, …, n_dim, …n_k), the each n_dim-element vector v along dimension dim is transformed as … and the equation.

Each subtensor is flattened into a vector, i.e. ∥v∥p\lVert v \rVert_p∥v∥p​ is not a matrix norm.

This sentence seems to be particularly misleading, and I would suggest to strike it - given that the things that are normed are one-dimensional, how could they be a matrix norm.
Best regards
Thomas
Edit: P.S.: I made this a quick PR. 56 Thank you, @alpapado, for your feedback on the documentation! It helps us improve.