Theorems · Theorem · linear algebra

LinearMap.nilRank_le_natTrailingDegree_charpoly

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup L] [inst_2 : Module R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] (φ : L →ₗ[R] Module.End R M) [inst_5 : Module.Free R M]
  [inst_6 : Module.Finite R M] [inst_7 : Module.Finite R L] [inst_8 : Module.Free R L] [Nontrivial R] (x : L),
  φ.nilRank ≤ (LinearMap.charpoly (φ x)).natTrailingDegree

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

3 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleModule.FreeModule.FiniteModule.FiniteModule.FreeNontrivial