Theorems · Definition · geometry

AffineIsometry.linearIsometry

{𝕜 : Type u_1} →
  {V : Type u_2} →
    {V₂ : Type u_5} →
      {P : Type u_10} →
        {P₂ : Type u_11} →
          [inst : NormedField 𝕜] →
            [inst_1 : SeminormedAddCommGroup V] →
              [inst_2 : NormedSpace 𝕜 V] →
                [inst_3 : PseudoMetricSpace P] →
                  [inst_4 : NormedAddTorsor V P] →
                    [inst_5 : SeminormedAddCommGroup V₂] →
                      [inst_6 : NormedSpace 𝕜 V₂] →
                        [inst_7 : PseudoMetricSpace P₂] → [inst_8 : NormedAddTorsor V₂ P₂] → (P →ᵃⁱ[𝕜] P₂) → V →ₗᵢ[𝕜] V₂

The underlying linear map of an affine isometry is in fact a linear isometry.

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

13 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor