Theorems · Theorem · linear algebra

Module.End.independent_iInf_maxGenEigenspace_of_forall_mapsTo

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  (f : ι → Module.End R M) [IsDomain R] [Module.IsTorsionFree R M],
  (∀ (i j : ι) (φ : R), Set.MapsTo ⇑(f i) ↑((f j).maxGenEigenspace φ) ↑((f j).maxGenEigenspace φ)) →
    iSupIndep fun χ => ⨅ i, (f i).maxGenEigenspace (χ i)

Defined in

Mathlib.LinearAlgebra.Eigenspace.Pi

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsDomainModule.IsTorsionFree