Theorems · Definition · geometry

AffineEquiv.ofLinearEquiv

{k : Type u_10} →
  {V : Type u_11} →
    {P : Type u_12} →
      [inst : Ring k] →
        [inst_1 : AddCommGroup V] → [inst_2 : Module k V] → [inst_3 : AddTorsor V P] → (V ≃ₗ[k] V) → P → P → P ≃ᵃ[k] P

Construct an affine equivalence from a linear equivalence and two base points. Given a linear equivalence A : V ≃ₗ[k] V and base points p₀ p₁ : P, this constructs the affine equivalence T x = A (x -ᵥ p₀) +ᵥ p₁. This is the standard way to convert a linear automorphism into an affine automorphism with specified base point mapping.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

4 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor