Theorems · Theorem · linear algebra
LinearMap.trace_lie
∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(f g : Module.End R M), (LinearMap.trace R M) ⁅f, g⁆ = 0- Defined in
- Mathlib.LinearAlgebra.Trace
- Cited by
- 3 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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- sub_selfproof · cited by 996
- Module.Endstatement and proof · cited by 774
- Bracket.bracketstatement · cited by 642
- map_subproof · cited by 565
- LinearMap.tracestatement and proof · cited by 87
- LinearMap.trace_mul_commproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.trace_toEnd_eq_zeroproof · cited by 1
- LieModule.trace_toEnd_eq_zero_of_mem_lcsproof · cited by 1
- LieModule.trace_toEnd_genWeightSpaceChain_eq_zeroproof · cited by 1