det_rotation — Mathlib

English

rotationOf(rotation a) equals a, i.e., returning from rotation through rotation yields the original circle element.

Русский

rotationOf(rotation a) равно a; возвращение из rotation через rotation возвращает исходный элемент окружности.

LaTeX

$$$rotationOf( rotation(a) ) = a$$$

Lean4

/-- The determinant of `rotation` (as a linear map) is equal to `1`. -/
@[simp]
theorem det_rotation (a : Circle) : LinearMap.det ((rotation a).toLinearEquiv : ℂ →ₗ[ℝ] ℂ) = 1 :=
  by
  rw [← LinearMap.det_toMatrix basisOneI, toMatrix_rotation, Matrix.det_fin_two]
  simp [← normSq_apply]

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