Theorems · Definition · functional analysis
Complex.orthonormalBasisOneI
OrthonormalBasis (Fin 2) ℝ ℂ
![1, I] is an orthonormal basis for ℂ considered as a real inner product space.
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 10 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement · cited by 5,565
- OrthonormalBasisstatement · cited by 188
- Complex.basisOneIproof · cited by 16
- Module.Basis.toOrthonormalBasisproof · cited by 5
Cited by12
Results whose statement or proof uses this declaration.
- Complex.isometryOfOrthonormalproof · cited by 3
- Complex.areaFormproof · cited by 3
- Complex.volume_preserving_equiv_piproof · cited by 2
- InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlaneproof · cited by 2
- NumberField.mixedEmbedding.euclidean.stdOrthonormalBasisproof · cited by 2
- Complex.coe_orthonormalBasisOneIstatement · cited by 2
- Complex.toBasis_orthonormalBasisOneIstatement · cited by 1
- InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlaneproof · cited by 0
- Complex.isometryOfOrthonormal_applyproof · cited by 0
- Complex.orthonormalBasisOneI_repr_applystatement · cited by 0
- Complex.orthonormalBasisOneI_repr_symm_applystatement · cited by 0
- Complex.map_isometryOfOrthonormalproof · cited by 0