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Theorems · Theorem · functional analysis

Orthonormal.comp

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {ι : Type u_4} {ι' : Type u_5} {v : ι → E},
  Orthonormal 𝕜 v → ∀ (f : ι' → ι), Function.Injective f → Orthonormal 𝕜 (v ∘ f)

A subfamily of an orthonormal family (i.e., a composition with an injective map) is an orthonormal family.

Defined in
Mathlib.Analysis.InnerProductSpace.Orthonormal
Cited by
2 results in Mathlib
Foundations
Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeSeminormedAddCommGroupInnerProductSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Orthonormal.exists_orthonormalBasis_extension · cited by 2Orthonormal.exists_orthon…orthonormal_subtype_range · cited by 2orthonormal_subtype_rangeInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupInner.inner · cited by 1089Inner.innerOrthonormal · cited by 85Orthonormalorthonormal_iff_ite · cited by 15orthonormal_iff_iteOrthonormal.compCITED BYCITES

Cites6

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Cited by2

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