Theorems · Theorem · linear algebra
Module.End.finite_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), (spectrum K f).FiniteAn endomorphism of a finite-dimensional vector space has a finite spectrum.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Minpoly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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
- Set.ofPredproof · cited by 6,101
- Set.extproof · cited by 2,266
- FiniteDimensionalstatement and proof · cited by 1,854
- Set.Finitestatement and proof · cited by 1,814
- Module.Endstatement and proof · cited by 774
- spectrumstatement and proof · cited by 510
- Module.End.HasEigenvalueproof · cited by 56
- Module.End.hasEigenvalue_iff_mem_spectrumproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.finite_spectrumproof · cited by 1