Theorems · Definition · geometry

LinearIsometryEquiv.toAffineIsometryEquiv

{𝕜 : Type u_1} →
  {V : Type u_2} →
    {V₂ : Type u_5} →
      [inst : NormedField 𝕜] →
        [inst_1 : SeminormedAddCommGroup V] →
          [inst_2 : NormedSpace 𝕜 V] →
            [inst_3 : SeminormedAddCommGroup V₂] → [inst_4 : NormedSpace 𝕜 V₂] → (V ≃ₗᵢ[𝕜] V₂) → V ≃ᵃⁱ[𝕜] V₂

Reinterpret a linear isometry equiv as an affine isometry equiv.

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

6 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpace