Theorems · Theorem · linear algebra
Module.End.exists_hasEigenvalue_of_genEigenspace_eq_top
∀ {R : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Nontrivial M]
{f : Module.End R M} (k : ℕ∞), ⨆ μ, (f.genEigenspace μ) k = ⊤ → ∃ μ, f.HasEigenvalue μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- ENatstatement and proof · cited by 4,985
- Bot.botproof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- iSupstatement and proof · cited by 2,415
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.exists_nontrivial_weightSpace_of_lieIdealproof · cited by 0