Theorems · Theorem · functional analysis
Orthonormal.nnnorm_eq_one
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{ι : Type u_4} {v : ι → E}, Orthonormal 𝕜 v → ∀ (i : ι), ‖v i‖₊ = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Nat.cast_oneproof · cited by 2,501
- NNReal.toRealproof · cited by 1,260
- NNNorm.nnnormstatement and proof · cited by 952
- Orthonormalstatement and proof · cited by 85
- Orthonormal.norm_eq_oneproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- OrthonormalBasis.nnnorm_eq_oneproof · cited by 0