Theorems · Definition · geometry

Orientation.basisRightAngleRotation

{E : Type u_1} →
  [inst : NormedAddCommGroup E] →
    [inst_1 : InnerProductSpace ℝ E] →
      [Fact (Module.finrank ℝ E = 2)] → Orientation ℝ E (Fin 2) → (x : E) → x ≠ 0 → Module.Basis (Fin 2) ℝ E

For a nonzero vector x in an oriented two-dimensional real inner product space E, ![x, J x] forms an (orthogonal) basis for E.

Defined in

Mathlib.Analysis.InnerProductSpace.TwoDim

Cited by

8 results in Mathlib

Foundations

Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact