Theorems · Theorem · linear algebra
LinearMap.charpoly_eq_X_pow_iff
∀ {R : Type u_1} {M : Type u_3} [inst : CommRing R] [IsDomain R] [inst_2 : AddCommGroup M] [inst_3 : Module R M]
[inst_4 : Module.Finite R M] [inst_5 : Module.Free R M] [IsNoetherian R M] (φ : Module.End R M),
LinearMap.charpoly φ = Polynomial.X ^ Module.finrank R M ↔ ∀ (m : M), ∃ n, (φ ^ n) m = 0- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Zero
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 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 and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Polynomialstatement · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Module.finrankstatement and proof · cited by 1,770
- Polynomial.Xstatement and proof · cited by 1,639
- Module.Finitestatement and proof · cited by 1,032
- Module.Endstatement and proof · cited by 774
- Module.Freestatement and proof · cited by 597
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1