Theorems · Theorem · functional analysis
Module.Basis.coe_toOrthonormalBasis_repr
∀ {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] (v : Module.Basis ι 𝕜 E) (hv : Orthonormal 𝕜 ⇑v),
⇑(v.toOrthonormalBasis hv).repr = ⇑(v.equivFun ≪≫ₗ (WithLp.linearEquiv 2 𝕜 (ι → 𝕜)).symm)- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
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- 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
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- Module.Basisstatement and proof · cited by 1,477
- LinearEquiv.symmstatement · cited by 1,461
- LinearIsometryEquivstatement · cited by 748
- WithLpstatement · cited by 345
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