Theorems · Theorem · linear algebra
realPart_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), ↑(realPart a) = 2⁻¹ • (a + star a)- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- 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
- StarModulestatement and proof · cited by 570
- StarAddMonoidstatement and proof · cited by 296
- smul_addproof · cited by 263
Cited by9
Results whose statement or proof uses this declaration.
- cfc_re_idproof · cited by 4
- cfcₙ_re_idproof · cited by 4
- realPart_I_smulproof · cited by 4
- realPart.norm_leproof · cited by 2
- imaginaryPart_I_smulproof · cited by 2
- CStarAlgebra.norm_smul_two_inv_smul_add_four_unitaryproof · cited by 1
- realPart_ofRealproof · cited by 1
- realPart_oneproof · cited by 0
- map_realPartproof · cited by 0