Theorems · Theorem · linear algebra
Module.End.isRoot_of_hasEigenvalue
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsDomain R]
[Module.IsTorsionFree R M] {f : Module.End R M} {μ : R}, f.HasEigenvalue μ → (minpoly R f).IsRoot μ- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Minpoly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · 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
- IsDomainstatement and proof · cited by 2,196
- Module.Endstatement and proof · cited by 774
- Module.IsTorsionFreestatement and proof · cited by 600
- minpolystatement · cited by 439
- Polynomial.IsRootstatement · cited by 152
- minpoly.aevalproof · cited by 91
- Module.End.genEigenspaceproof · cited by 70
- Module.End.HasEigenvaluestatement and proof · cited by 56
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.hasEigenvalue_iff_isRootproof · cited by 1