Theorems · Theorem · linear algebra
imaginaryPart_apply_coe
∀ {A : Type u_1} [inst : AddCommGroup A] [inst_1 : Module ℂ A] [inst_2 : StarAddMonoid A] [inst_3 : StarModule ℂ A]
(a : A), ↑(imaginaryPart a) = -Complex.I • 2⁻¹ • (a - star a)- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- Star.starstatement and proof · cited by 1,082
- Complex.Istatement and proof · cited by 866
- StarModulestatement and proof · cited by 570
- neg_smulproof · cited by 306
Cited by6
Results whose statement or proof uses this declaration.
- realPart_I_smulproof · cited by 4
- imaginaryPart_I_smulproof · cited by 2
- imaginaryPart_ofRealproof · cited by 1
- skewAdjointPart_eq_I_smul_imaginaryPartproof · cited by 0
- isStarNormal_iff_forall_exp_mul_exp_mem_unitaryproof · cited by 0
- map_imaginaryPartproof · cited by 0