Theorems · Theorem · linear algebra
LinearMap.isNilpotent_trace_of_isNilpotent
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {f : M →ₗ[R] M},
IsNilpotent f → IsNilpotent ((LinearMap.trace R M) f)- Defined in
- Mathlib.LinearAlgebra.Trace
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 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
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Module.Basisproof · cited by 1,477
- IsNilpotentstatement and proof · cited by 248
- LinearMap.tracestatement · cited by 87
- LinearMap.trace_eq_matrix_traceproof · cited by 14
- IsNilpotent.zeroproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- LieModule.trace_toEnd_genWeightSpaceproof · cited by 3
- LieModule.traceForm_eq_zero_of_isNilpotentproof · cited by 1
- LinearMap.trace_comp_eq_mul_of_commute_of_isNilpotentproof · cited by 1
- LieAlgebra.IsKilling.eq_zero_of_isNilpotent_ad_of_mem_isCartanSubalgebraproof · cited by 1
- Algebra.isNilpotent_trace_of_isNilpotentproof · cited by 1