Theorems · Theorem · linear algebra
Module.End.hasEigenvalue_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.HasEigenvalue μ ↔ μ ∈ spectrum K f- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.Endstatement and proof · cited by 774
- spectrumstatement · cited by 510
- Module.End.HasEigenvaluestatement · cited by 56
- Module.End.hasUnifEigenvalue_iff_mem_spectrumproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- spectrum_diagonalproof · cited by 2
- Module.End.finite_spectrumproof · cited by 1
- Module.End.HasEigenvalue.of_mem_spectrumproof · cited by 0
- Module.End.mem_spectrum_iff_isRoot_charpolyproof · cited by 0