Theorems · Definition · functional analysis

Orthonormal

(𝕜 : Type u_1) →
  {E : Type u_2} →
    [inst : RCLike 𝕜] → [inst_1 : SeminormedAddCommGroup E] → [InnerProductSpace 𝕜 E] → {ι : Type u_4} → (ι → E) → Prop

An orthonormal set of vectors in an InnerProductSpace

Defined in: Mathlib.Analysis.InnerProductSpace.Orthonormal
Cited by: 85 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike SeminormedAddCommGroup InnerProductSpace

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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.

Norm.normproof · 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
Inner.innerproof · cited by 1,089
Pairwiseproof · cited by 516

Cited by95

Results whose statement or proof uses this declaration.

orthonormal_iff_itestatement and proof · cited by 15
OrthonormalBasis.orthonormalstatement · cited by 14
Orthonormal.equivstatement and proof · cited by 7
Module.Basis.toBasis_toOrthonormalBasisstatement and proof · cited by 7
Module.Basis.coe_toOrthonormalBasisstatement and proof · cited by 6
Orthonormal.linearIndependentstatement and proof · cited by 5
Module.Basis.toOrthonormalBasisstatement and proof · cited by 5
Orthonormal.norm_eq_onestatement and proof · cited by 4
HilbertBasis.coe_mkstatement and proof · cited by 4
Orthonormal.equiv_applystatement and proof · cited by 3
Orthonormal.inner_right_finsuppstatement and proof · cited by 3
OrthonormalBasis.coe_mkstatement and proof · cited by 3