Theorems · Theorem · linear algebra
Module.End.HasUnifEigenvalue.exists_hasUnifEigenvector
∀ {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} {k : ℕ∞}, f.HasUnifEigenvalue μ k → ∃ v, f.HasUnifEigenvector μ k v- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 3 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.
Cites8
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
- ENatstatement and proof · cited by 4,985
- Module.Endstatement and proof · cited by 774
- Module.End.HasUnifEigenvaluestatement and proof · cited by 18
- Submodule.exists_mem_ne_zero_of_ne_botproof · cited by 9
- Module.End.HasUnifEigenvectorstatement · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Module.End.HasUnifEigenvalue.isNilpotent_of_isNilpotentproof · cited by 1
- Module.End.HasUnifEigenvalue.mem_spectrumproof · cited by 1
- Module.End.HasUnifEigenvalue.powproof · cited by 1