Theorems · Definition · geometry

Orientation.rightAngleRotation

{E : Type u_2} →
  [inst : NormedAddCommGroup E] →
    [inst_1 : InnerProductSpace ℝ E] → [Fact (Module.finrank ℝ E = 2)] → Orientation ℝ E (Fin 2) → E ≃ₗᵢ[ℝ] E

An isometric automorphism of an oriented real inner product space of dimension 2 (usual notation J). This automorphism squares to -1. We will define rotations in such a way that this automorphism is equal to rotation by 90 degrees.

Defined in

Mathlib.Analysis.InnerProductSpace.TwoDim

Cited by

43 results in Mathlib

Foundations

Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact