Theorems · Theorem · functional analysis
OrthonormalBasis.coe_reindex
∀ {ι : Type u_1} {ι' : Type u_2} {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 : Fintype ι'] (b : OrthonormalBasis ι 𝕜 E) (e : ι ≃ ι'),
⇑(b.reindex e) = ⇑b ∘ ⇑e.symm- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 6 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Equiv.symmstatement · cited by 3,681
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- OrthonormalBasisstatement and proof · cited by 188
- OrthonormalBasis.reindexstatement · cited by 15
- OrthonormalBasis.reindex_applyproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Orientation.measure_orthonormalBasisproof · cited by 2
- Orthonormal.exists_orthonormalBasis_extension_of_card_eqproof · cited by 1
- OrthonormalBasis.repr_reindexproof · cited by 1
- parallelepiped_orthonormalBasis_one_dimproof · cited by 1
- DirectSum.IsInternal.subordinateOrthonormalBasis_subordinateproof · cited by 0
- LinearMap.toMatrixOrthonormal_reindexproof · cited by 0