feat(analysis/conformal/inner_product_space): the inversion map of a normed space and its conformality #9626
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justadzr
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hrmacbeth
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Oct 9, 2021
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| lemma fderiv_inversion {X : Type*} [inner_product_space ℝ X] | ||
| {r : ℝ} (hr : 0 < r) {x₀ : X} {y x : X} (hx : x ≠ x₀) : | ||
| fderiv ℝ (inversion hr x₀) x y = r • (∥x - x₀∥ ^ 4)⁻¹ • |
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Please make a has_fderiv_at version, and deduce the fderiv version from it!
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I am not sure in what context the inversion map should be. I've only read about the maps as
x-> x/|x|^2due to my poor mathematical background. Thanks in advance for any suggestions/guidance.