Theorems · Theorem · functional analysis
Orthonormal.norm_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
- 4 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Orthonormalstatement and proof · cited by 85
Cited by4
Results whose statement or proof uses this declaration.
- orthonormal_iff_iteproof · cited by 15
- OrthonormalBasis.norm_eq_oneproof · cited by 3
- Orthonormal.enorm_eq_oneproof · cited by 1
- Orthonormal.nnnorm_eq_oneproof · cited by 1