Theorems · Definition · functional analysis
EuclideanSpace.single
{ι : Type u_1} → {𝕜 : Type u_3} → [RCLike 𝕜] → [DecidableEq ι] → ι → 𝕜 → EuclideanSpace 𝕜 ιThe vector given in Euclidean space by being a : 𝕜 at coordinate i : ι and 0 : 𝕜 at
all other coordinates.
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- EuclideanSpacestatement · cited by 307
- PiLp.singleproof · cited by 24
Cited by22
Results whose statement or proof uses this declaration.
- OrthonormalBasis.orthonormalproof · cited by 14
- OrthonormalBasis.repr_selfstatement and proof · cited by 4
- EuclideanSpace.basisFun_applystatement · cited by 4
- OrthonormalBasis.reindex_applyproof · cited by 3
- OrthonormalBasis.repr_symm_singlestatement and proof · cited by 3
- EuclideanSpace.inner_single_leftstatement · cited by 3
- OrthonormalBasis.coe_ofReprstatement and proof · cited by 2
- EuclideanSpace.piLpCongrLeft_singlestatement · cited by 1
- Matrix.inner_toEuclideanCLMproof · cited by 1
- EuclideanSpace.inner_single_rightstatement · cited by 1
- EuclideanSpace.nndist_single_samestatement · cited by 0
- EuclideanSpace.nnnorm_singlestatement · cited by 0