Theorems · Theorem · functional analysis
OrthonormalBasis.orthogonalProjection_eq_sum_rankOne
Deprecated since 2026-05-05Use OrthonormalBasis.orthogonalProjectionOnto_eq_sum_rankOne instead.
∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι] {U : Submodule 𝕜 E} [inst_4 : U.HasOrthogonalProjection]
(b : OrthonormalBasis ι 𝕜 ↥U), U.orthogonalProjectionOnto = ∑ i, ((InnerProductSpace.rankOne 𝕜) (b i)) ↑(b i)Alias of OrthonormalBasis.orthogonalProjectionOnto_eq_sum_rankOne.
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement · cited by 15,752
- Fintypestatement · cited by 7,736
- Submodulestatement · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- Finset.sumstatement · cited by 5,195
- InnerProductSpacestatement · cited by 3,523
- Finset.univstatement · cited by 3,473
- RCLikestatement · cited by 2,829
- starRingEndstatement · cited by 671
- Submodule.HasOrthogonalProjectionstatement · cited by 245
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.