Theorems · Theorem · linear algebra
Module.End.genEigenspace_le_genEigenspace_finrank
∀ {K : Type v} {V : Type w} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
(f : Module.End K V) (μ : K) (k : ℕ∞), (f.genEigenspace μ) k ≤ (f.genEigenspace μ) ↑(Module.finrank K V)Every generalized eigenvector is a generalized eigenvector for exponent finrank K V.
(Lemma 8.20 of [axler2024])
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- ENatstatement and proof · cited by 4,985
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
- le_topproof · cited by 411
Cited by2
Results whose statement or proof uses this declaration.
- Module.End.genEigenspace_eq_genEigenspace_finrank_of_leproof · cited by 1
- Module.End.maxGenEigenspace_eq_genEigenspace_finrankproof · cited by 0