Theorems · Theorem · geometry

Orientation.det_rotation

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) (θ : Real.Angle), LinearMap.det ↑(o.rotation θ).toLinearEquiv = 1

The determinant of rotation (as a linear map) is equal to 1.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

1 results in Mathlib

Foundations

Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact