Theorems · Theorem · linear algebra
Module.End.hasEigenvalue_iff_isRoot
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {f : Module.End R M}
{μ : R} [IsDomain R] [Module.Finite R M] [Module.IsTorsionFree R M], f.HasEigenvalue μ ↔ (minpoly R f).IsRoot μ- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Minpoly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.Finitestatement and proof · cited by 1,032
- Module.Endstatement and proof · cited by 774
- Module.IsTorsionFreestatement and proof · cited by 600
- minpolystatement · cited by 439
- Polynomial.IsRootstatement · cited by 152
- Module.End.HasEigenvaluestatement · cited by 56
- Module.End.hasEigenvalue_of_isRootproof · cited by 2
- Module.End.isRoot_of_hasEigenvalueproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.hasEigenvalue_zero_tfaeproof · cited by 2