Theorems · Theorem · linear algebra
Module.End.genEigenspace_le_smul
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f : Module.End R M)
(μ t : R) (k : ℕ∞), (f.genEigenspace μ) k ≤ ((t • f).genEigenspace (t * μ)) k- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites15
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
- Submodulestatement · cited by 7,192
- ENatstatement and proof · cited by 4,985
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
- smul_zeroproof · cited by 665
- SemigroupAction.mul_smulproof · cited by 291
- smul_subproof · cited by 142
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.map_smul_of_iInf_genEigenspace_ne_botproof · cited by 0