Theorems · Definition · complex analysis
Complex.ofRealCLM
ℝ →L[ℝ] ℂ
Continuous linear map version of the canonical embedding of ℝ in ℂ.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ContinuousLinearMapstatement · cited by 5,352
- LinearIsometry.toContinuousLinearMapproof · cited by 47
- Complex.ofRealLIproof · cited by 7
Cited by41
Results whose statement or proof uses this declaration.
- Orientation.kahlerproof · cited by 39
- NumberField.mixedEmbedding.mixedSpaceOfRealSpaceproof · cited by 20
- HasDerivAt.comp_ofRealproof · cited by 11
- Function.Complex.hasTemperateGrowth_ofRealproof · cited by 10
- HasDerivAt.real_of_complexproof · cited by 7
- HasStrictDerivAt.real_of_complexproof · cited by 6
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- HarmonicAt.differentiableAt_complex_partialproof · cited by 3
- analyticOnNhd_circleMapproof · cited by 3
- HasDerivAt.ofReal_compproof · cited by 3
- Real.hasFDerivAt_fourierChar_neg_bilinear_rightstatement and proof · cited by 3
- hasDerivAt_circleMapproof · cited by 3