Theorems · Theorem · functional analysis

Orientation.volumeForm_map

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] {n : ℕ}
  [_i : Fact (Module.finrank ℝ E = n)] (o : Orientation ℝ E (Fin n)) {F : Type u_2} [inst_2 : NormedAddCommGroup F]
  [inst_3 : InnerProductSpace ℝ F] [inst_4 : Fact (Module.finrank ℝ F = n)] (φ : E ≃ₗᵢ[ℝ] F) (x : Fin n → F),
  ((Orientation.map (Fin n) φ.toLinearEquiv) o).volumeForm x = o.volumeForm (⇑φ.symm ∘ x)

Defined in

Mathlib.Analysis.InnerProductSpace.Orientation

Cited by

2 results in Mathlib

Foundations

Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFactNormedAddCommGroupInnerProductSpaceFact