Theorems · Theorem · geometry

Orientation.areaForm_def

∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : Fact (Module.finrank ℝ E = 2)]
  (o : Orientation ℝ E (Fin 2)),
  o.areaForm =
    have z := AlternatingMap.constLinearEquivOfIsEmpty.symm;
    have y := (LinearMap.llcomp ℝ E (E [⋀^Fin 0]→ₗ[ℝ] ℝ) ℝ) ↑z ∘ₗ AlternatingMap.curryLeftLinearMap;
    y ∘ₗ AlternatingMap.curryLeftLinearMap o.volumeForm

Defined in

Mathlib.Analysis.InnerProductSpace.TwoDim

Cited by

1 results in Mathlib

Foundations

Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact