Theorems · Theorem · linear algebra

Module.End.exists_ker_pow_eq_ker_pow_succ

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [FiniteDimensional K V] (f : Module.End K V),
  ∃ k ≤ Module.finrank K V, LinearMap.ker (f ^ k) = LinearMap.ker (f ^ k.succ)

Defined in: Mathlib.LinearAlgebra.FiniteDimensional.Lemmas
Cited by: 1 results in Mathlib
Foundations: Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module FiniteDimensional

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Cites16

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

Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
Submodulestatement · cited by 7,192
LE.le.transproof · cited by 3,151
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankstatement and proof · cited by 1,770
DivisionRingstatement and proof · cited by 1,062
LinearMap.kerstatement and proof · cited by 848
Module.Endstatement and proof · cited by 774
zero_leproof · cited by 382
lt_of_le_of_neproof · cited by 230

Cited by1

Results whose statement or proof uses this declaration.

Module.End.ker_pow_eq_ker_pow_finrank_of_leproof · cited by 1