Theorems · Theorem · linear algebra
IsSelfAdjoint.coe_realPart
∀ {A : Type u_1} [inst : AddCommGroup A] [inst_1 : Module ℂ A] [inst_2 : StarAddMonoid A] [inst_3 : StarModule ℂ A]
{x : A}, IsSelfAdjoint x → ↑(realPart x) = x- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 6 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.
Cites14
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
- StarModulestatement and proof · cited by 570
- IsSelfAdjointstatement and proof · cited by 545
- StarAddMonoidstatement and proof · cited by 296
- selfAdjointstatement · cited by 135
Cited by6
Results whose statement or proof uses this declaration.
- nonneg_iff_realPart_imaginaryPartproof · cited by 3
- selfAdjoint.realPart_coeproof · cited by 2
- realPart_surjectiveproof · cited by 0
- imaginaryPart_surjectiveproof · cited by 0
- realPart_idemproof · cited by 0
- realPart_imaginaryPartproof · cited by 0