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analysis.inner_product_space.conformal_linear_map

Conformal maps between inner product spaces #

In an inner product space, a map is conformal iff it preserves inner products up to a scalar factor.

theorem is_conformal_map_iff {E : Type u_1} {F : Type u_2} [inner_product_space E] [inner_product_space F] (f : E →L[] F) :
is_conformal_map f ∃ (c : ), 0 < c ∀ (u v : E), has_inner.inner (f u) (f v) = c * has_inner.inner u v

A map between two inner product spaces is a conformal map if and only if it preserves inner products up to a scalar factor, i.e., there exists a positive c : ℝ such that ⟪f u, f v⟫ = c * ⟪u, v⟫ for all u, v.