Theorems · Definition · functional analysis
OrthonormalBasis.singleton
(ι : Type u_7) → (𝕜 : Type u_8) → [inst : Unique ι] → [inst_1 : RCLike 𝕜] → OrthonormalBasis ι 𝕜 𝕜
OrthonormalBasis.singleton ι 𝕜 is the orthonormal basis sending the unique element of ι to
1 : 𝕜.
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RCLikestatement and proof · cited by 2,829
- Uniquestatement and proof · cited by 400
- OrthonormalBasisstatement · cited by 188
- Module.Basis.singletonproof · cited by 15
- Module.Basis.toOrthonormalBasisproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- OrthonormalBasis.singleton_applystatement · cited by 3
- InnerProductSpace.laplacianWithin_eq_iteratedDerivWithin_realproof · cited by 1
- OrthonormalBasis.toBasis_singletonstatement · cited by 1
- OrthonormalBasis.coe_singletonstatement · cited by 1
- InnerProductSpace.toMatrix_rankOneproof · cited by 0
- InnerProductSpace.trace_rankOneproof · cited by 0
- OrthonormalBasis.singleton_reprstatement · cited by 0