Theorems · Theorem · linear algebra

Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNil

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {f g : Module.End R M} {μ : R} {k : ℕ∞} {m : M},
  m ∈ (f.genEigenspace μ) k → Commute f g → g.IsFinitelySemisimple → IsNilpotent (f - g) → g m = μ • m

Defined in

Mathlib.LinearAlgebra.Eigenspace.Semisimple

Cited by

2 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule