Theorems · Theorem · linear algebra
Module.End.hasEigenvalue_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}, f.HasEigenvector μ x → f.HasEigenvalue μ- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 69 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.
Cites7
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.HasEigenvaluestatement · cited by 56
- Module.End.HasEigenvectorstatement and proof · cited by 23
- Module.End.HasUnifEigenvector.hasUnifEigenvalueproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.orthogonalFamily_eigenspacesproof · cited by 3
- LinearMap.IsSymmetric.hasEigenvalue_eigenvaluesproof · cited by 3
- Module.End.hasEigenvalue_of_isRootproof · cited by 2
- LinearMap.hasEigenvalue_zero_tfaeproof · cited by 2
- hasEigenvalue_toLin_diagonal_iffproof · cited by 1
- LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensionalproof · cited by 1
- IsCompactOperator.antilipschitz_of_not_hasEigenvalueproof · cited by 1
- LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensionalproof · cited by 0