Theorems · Theorem · linear algebra
Module.End.hasUnifEigenvalue_iff_mem_spectrum
∀ {K : Type v} {V : Type w} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
{f : Module.End K V} {μ : K}, f.HasUnifEigenvalue μ 1 ↔ μ ∈ spectrum K f- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- ENatstatement · cited by 4,985
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- FiniteDimensionalstatement and proof · cited by 1,854
- LinearMap.kerproof · cited by 848
- Module.Endstatement and proof · cited by 774
Cited by2
Results whose statement or proof uses this declaration.
- Module.End.hasEigenvalue_iff_mem_spectrumproof · cited by 4
- Module.End.HasUnifEigenvalue.of_mem_spectrumproof · cited by 0