rightAngleRotation — Mathlib

English

There is a real-linear isometry J on E which serves as the 90-degree rotation and satisfies J^2 = −Id_E; J preserves norms and rotates by 90 degrees in the oriented 2D space.

Русский

Существует линейная изометрия J на E, являющаяся поворотом на 90 градусов и удовлетворяющая J^2 = −Id_E; она сохраняет нормы.

LaTeX

$$$J^2 = -\\\\mathrm{Id}_E$$$

Lean4

/-- 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. -/
def rightAngleRotation :=
  val_proj @wrapped✝.{}

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