Theorems · Theorem · linear algebra

Module.End.mem_iInf_maxGenEigenspace_iff

∀ {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) (χ : ι → R) (m : M),
  m ∈ ⨅ i, (f i).maxGenEigenspace (χ i) ↔ ∀ (j : ι), ∃ k, ((f j - χ j • 1) ^ k) m = 0

Defined in: Mathlib.LinearAlgebra.Eigenspace.Pi
Cited by: 1 results in Mathlib
Foundations: Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Submodulestatement · cited by 7,192
iInfstatement · cited by 1,690
Module.Endstatement and proof · cited by 774
Module.End.maxGenEigenspacestatement and proof · cited by 41

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Module.End.independent_iInf_maxGenEigenspace_of_forall_mapsToproof · cited by 1