Theorems · Definition · complex analysis
Complex.conjLIE
ℂ ≃ₗᵢ[ℝ] ℂ
The complex-conjugation function from ℂ to itself is an isometric linear equivalence.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- Complexstatement · cited by 5,565
- LinearIsometryEquivstatement · cited by 748
- AlgEquiv.toLinearEquivproof · cited by 117
- Complex.conjAeproof · cited by 16
- Complex.norm_conjproof · cited by 8
Cited by13
Results whose statement or proof uses this declaration.
- Complex.conjCAEproof · cited by 27
- Complex.isometry_conjproof · cited by 2
- Complex.conjCLE_normproof · cited by 2
- linear_isometry_complexstatement and proof · cited by 1
- linear_isometry_complex_auxstatement and proof · cited by 1
- isConformalMap_conjstatement and proof · cited by 1
- IsConformalMap.is_complex_or_conj_linearproof · cited by 1
- Complex.det_conjLIEstatement · cited by 0
- Complex.linearEquiv_det_conjLIEstatement · cited by 0
- rotation_ne_conjLIEstatement and proof · cited by 0
- Complex.conjLIE_applystatement · cited by 0
- Complex.conjLIE_symmstatement · cited by 0