Theorems · Theorem · functional analysis
HilbertBasis.repr_self
∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : DecidableEq ι] (b : HilbertBasis ι 𝕜 E) (i : ι),
b.repr (b i) = lp.single 2 i 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 233 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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement · cited by 9,879
- InnerProductSpacestatement and proof · cited by 3,523
- AddSubgroupstatement · cited by 3,232
- RCLikestatement and proof · cited by 2,829
- LinearIsometryEquivstatement · cited by 748
- PreLpstatement · cited by 163
- lpstatement · cited by 157
- lp.singlestatement and proof · cited by 34
- HilbertBasisstatement and proof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- HilbertBasis.repr_apply_applyproof · cited by 6
- HilbertBasis.orthonormalproof · cited by 1
- HilbertBasis.hasSum_repr_symmproof · cited by 1