Theorems · Theorem · linear algebra
LinearMap.finrank_genEigenspace_le
∀ {K : Type u_2} {M : Type u_3} [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M]
[inst_3 : Module.Finite K M] (φ : Module.End K M) (μ : K) (k : ℕ),
Module.finrank K ↥((φ.genEigenspace μ) ↑k) ≤ Polynomial.rootMultiplicity μ (LinearMap.charpoly φ)- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Zero
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- ENatstatement · cited by 4,985
- le_reflproof · cited by 2,061
- Module.finrankstatement · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
- le_imp_le_of_le_of_leproof · cited by 576
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.finrank_eigenspace_leproof · cited by 0