Theorems · Theorem · functional analysis
Complex.orthonormalBasisOneI_repr_symm_apply
∀ (x : EuclideanSpace ℝ (Fin 2)), Complex.orthonormalBasisOneI.repr.symm x = ↑(x.ofLp 0) + ↑(x.ofLp 1) * Complex.I
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- ENNRealstatement · cited by 9,879
- Complexstatement · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- Complex.Istatement · cited by 866
- LinearIsometryEquivstatement · cited by 748
- WithLp.ofLpstatement · cited by 323
- EuclideanSpacestatement and proof · cited by 307
- LinearIsometryEquiv.symmstatement · cited by 287
- OrthonormalBasis.reprstatement · cited by 61
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