Theorems · Theorem · linear algebra
LinearMap.minpoly_dvd_charpoly
∀ {K : Type u} {M : Type v} [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M]
[inst_3 : FiniteDimensional K M] (f : M →ₗ[K] M), minpoly K f ∣ f.charpoly- Defined in
- Mathlib.LinearAlgebra.Charpoly.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- FiniteDimensionalstatement and proof · cited by 1,854
- minpolystatement · cited by 439
- LinearMap.charpolystatement · cited by 67
- minpoly.dvdproof · cited by 31
- LinearMap.aeval_self_charpolyproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.hasEigenvalue_zero_tfaeproof · cited by 2