Theorems · Definition · functional analysis

OrthonormalBasis.prod

{𝕜 : Type u_1} →
  {ι₁ : Type u_2} →
    {ι₂ : Type u_3} →
      {E : Type u_4} →
        {F : Type u_5} →
          [inst : RCLike 𝕜] →
            [inst_1 : NormedAddCommGroup E] →
              [inst_2 : InnerProductSpace 𝕜 E] →
                [inst_3 : NormedAddCommGroup F] →
                  [inst_4 : InnerProductSpace 𝕜 F] →
                    [inst_5 : Fintype ι₁] →
                      [inst_6 : Fintype ι₂] →
                        OrthonormalBasis ι₁ 𝕜 E →
                          OrthonormalBasis ι₂ 𝕜 F → OrthonormalBasis (ι₁ ⊕ ι₂) 𝕜 (WithLp 2 (E × F))

The product of two orthonormal bases is a basis for the L2-product.

Defined in

Mathlib.Analysis.InnerProductSpace.ProdL2

Cited by

1 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceFintypeFintype