Theorems · Definition · functional analysis

OrthonormalBasis.tensorProduct

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : RCLike 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : InnerProductSpace 𝕜 E] →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : InnerProductSpace 𝕜 F] →
                {ι₁ : Type u_6} →
                  {ι₂ : Type u_7} →
                    [inst_5 : Fintype ι₁] →
                      [inst_6 : Fintype ι₂] →
                        OrthonormalBasis ι₁ 𝕜 E →
                          OrthonormalBasis ι₂ 𝕜 F → OrthonormalBasis (ι₁ × ι₂) 𝕜 (TensorProduct 𝕜 E F)

The orthonormal basis of the tensor product of two orthonormal bases.

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

5 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceFintypeFintype