Theorems · Definition · linear algebra
Module.End.HasEigenvector
{R : Type v} →
{M : Type w} → [inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Module.End R M → R → M → PropA nonzero element of an eigenspace is an eigenvector. (Def 5.8 of [axler2024])
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 67 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.
Cites5
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
- Module.Endstatement and proof · cited by 774
- Module.End.HasUnifEigenvectorproof · cited by 7
Cited by23
Results whose statement or proof uses this declaration.
- Module.End.hasEigenvalue_of_hasEigenvectorstatement and proof · cited by 8
- Module.End.HasEigenvalue.exists_hasEigenvectorstatement · cited by 8
- Module.End.HasEigenvector.apply_eq_smulstatement and proof · cited by 3
- IsSelfAdjoint.hasEigenvector_of_isLocalExtrOnstatement · cited by 2
- hasEigenvector_toLin_diagonalstatement · cited by 2
- Module.End.aeval_apply_of_hasEigenvectorstatement and proof · cited by 2
- LinearMap.IsSymmetric.hasEigenvector_eigenvectorBasisstatement and proof · cited by 2
- Module.End.eigenvectors_linearIndependentstatement and proof · cited by 2
- IsSl2Triple.HasPrimitiveVectorWith.exists_natproof · cited by 2
- IsSelfAdjoint.hasEigenvector_of_isMaxOnstatement and proof · cited by 1
- IsSelfAdjoint.hasEigenvector_of_isMinOnstatement and proof · cited by 1
- Module.End.HasEigenvector.pow_applystatement and proof · cited by 1