Theorems · Theorem · linear algebra
realPart_I_smul
∀ {A : Type u_1} [inst : AddCommGroup A] [inst_1 : Module ℂ A] [inst_2 : StarAddMonoid A] [inst_3 : StarModule ℂ A]
(a : A), realPart (Complex.I • a) = -imaginaryPart a- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- SMulCommClassproof · cited by 1,927
- add_commproof · cited by 1,535
- Star.starproof · cited by 1,082
- sub_eq_add_negproof · cited by 1,023
Cited by4
Results whose statement or proof uses this declaration.
- imaginaryPart.norm_leproof · cited by 1
- selfAdjoint.realPart_unitarySelfAddISMulproof · cited by 1
- realPart_smulproof · cited by 0
- Complex.coe_realPartproof · cited by 0