Theorems · Theorem · linear algebra
Module.End.aeval_apply_of_hasEigenvector
∀ {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} {x : M} {p : Polynomial R}, f.HasEigenvector μ x → ((Polynomial.aeval f) p) x = Polynomial.eval μ p • x- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Minpoly
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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 and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
Cited by2
Results whose statement or proof uses this declaration.
- Module.End.isRoot_of_hasEigenvalueproof · cited by 1
- Module.End.aeval_apply_of_mem_apply_eq_smulproof · cited by 0