Theorems · Theorem · functional analysis
OrthonormalBasis.repr_self
∀ {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] [inst_4 : DecidableEq ι] (b : OrthonormalBasis ι 𝕜 E) (i : ι),
b.repr (b i) = EuclideanSpace.single i 1- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Fintypestatement and proof · cited by 7,736
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearIsometryEquivstatement · cited by 748
- EuclideanSpacestatement and proof · cited by 307
- OrthonormalBasisstatement and proof · cited by 188
- OrthonormalBasis.reprstatement and proof · cited by 61
- LinearIsometryEquiv.apply_symm_applyproof · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- OrthonormalBasis.orthonormalproof · cited by 14
- OrthonormalBasis.repr_apply_applyproof · cited by 11
- LinearMap.IsSymmetric.toMatrix_eigenvectorBasisproof · cited by 2
- OrthonormalBasis.equiv_apply_basisproof · cited by 2