Theorems · Theorem · functional analysis
OrthonormalBasis.sum_sq_norm_inner_left
∀ {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] (b : OrthonormalBasis ι 𝕜 E) (x : E),
∑ i, ‖inner 𝕜 x (b i)‖ ^ 2 = ‖x‖ ^ 2- 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- RCLikestatement and proof · cited by 2,829
- Finset.sum_congrproof · cited by 2,323
- Inner.innerstatement and proof · cited by 1,089
- OrthonormalBasisstatement and proof · cited by 188
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.