Theorems · Definition · functional analysis

LinearIsometry.rTensor

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      (G : Type u_4) →
        [inst : RCLike 𝕜] →
          [inst_1 : NormedAddCommGroup E] →
            [inst_2 : InnerProductSpace 𝕜 E] →
              [inst_3 : NormedAddCommGroup F] →
                [inst_4 : InnerProductSpace 𝕜 F] →
                  [inst_5 : NormedAddCommGroup G] →
                    [inst_6 : InnerProductSpace 𝕜 G] → (E →ₗᵢ[𝕜] F) → TensorProduct 𝕜 E G →ₗᵢ[𝕜] TensorProduct 𝕜 F G

This is the natural linear isometry induced by f : E ≃ₗᵢ F.

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

5 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace