Theorems · Theorem · linear algebra
imaginaryPart_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), imaginaryPart (Complex.I • a) = realPart a- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 2 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.
Cites30
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
- one_smulproof · cited by 1,374
- MulActionproof · cited by 1,294
- Star.starproof · cited by 1,082
Cited by2
Results whose statement or proof uses this declaration.
- imaginaryPart_surjectiveproof · cited by 0
- imaginaryPart_smulproof · cited by 0