Theorems · Theorem · geometry

Orientation.areaForm_map

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : Fact (Module.finrank ℝ E = 2)]
  (o : Orientation ℝ E (Fin 2)) {F : Type u_2} [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace ℝ F]
  [hF : Fact (Module.finrank ℝ F = 2)] (φ : E ≃ₗᵢ[ℝ] F) (x y : F),
  (((Orientation.map (Fin 2) φ.toLinearEquiv) o).areaForm x) y = (o.areaForm (φ.symm x)) (φ.symm y)

Defined in

Mathlib.Analysis.InnerProductSpace.TwoDim

Cited by

4 results in Mathlib

Foundations

Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFactNormedAddCommGroupInnerProductSpaceFact