Theorems · Theorem · functional analysis
EuclideanSpace.basisFun_apply
∀ (ι : Type u_1) (𝕜 : Type u_3) [inst : RCLike 𝕜] [inst_1 : Fintype ι] [inst_2 : DecidableEq ι] (i : ι), (EuclideanSpace.basisFun ι 𝕜) 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
- Assumes
- RCLikeFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- RCLikestatement and proof · cited by 2,829
- EuclideanSpacestatement · cited by 307
- OrthonormalBasisstatement · cited by 188
- EuclideanSpace.basisFunstatement · cited by 26
- EuclideanSpace.singlestatement · cited by 21
- PiLp.basisFun_applyproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covariance_eval_multivariateGaussianproof · cited by 3
- ProbabilityTheory.measurePreserving_restrict₂_multivariateGaussianproof · cited by 1
- Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitaryproof · cited by 1
- Matrix.inner_toEuclideanCLMproof · cited by 1