Theorems · Theorem · linear algebra
LinearMap.trace_lie_mul_eq
∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f g h : M →ₗ[R] M),
(LinearMap.trace R M) (⁅f, g⁆ * h) = (LinearMap.trace R M) (f * ⁅g, h⁆)- Defined in
- Mathlib.LinearAlgebra.Trace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- mul_assocproof · cited by 1,667
- Bracket.bracketstatement · cited by 642
- map_subproof · cited by 565
- mul_subproof · cited by 201
- sub_mulproof · cited by 170
- LinearMap.tracestatement and proof · cited by 87
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.trace_toEnd_mul_eq_zero_of_traceForm_eq_zeroproof · cited by 0