Theorems · Theorem · linear algebra
skewAdjoint.negISMul_apply_coe
∀ {A : Type u_1} [inst : AddCommGroup A] [inst_1 : Module ℂ A] [inst_2 : StarAddMonoid A] [inst_3 : StarModule ℂ A]
(a : ↥(skewAdjoint A)), ↑(skewAdjoint.negISMul a) = -Complex.I • ↑a- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 5 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 and proof · cited by 62,936
- Realstatement · 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
- Complex.Istatement · cited by 866
- StarModulestatement and proof · cited by 570
- StarAddMonoidstatement and proof · cited by 296
- selfAdjointstatement · cited by 135
Cited by5
Results whose statement or proof uses this declaration.
- realPart_add_I_smul_imaginaryPartproof · cited by 10
- imaginaryPart_apply_coeproof · cited by 6
- ker_imaginaryPartproof · cited by 1
- skewAdjoint.I_smul_neg_Iproof · cited by 0
- imaginaryPart_comp_subtype_selfAdjointproof · cited by 0