Theorems · Theorem · linear algebra

LinearMap.polyCharpoly_coeff_eq_zero_iff_of_basis

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} {ι : Type u_5} {ι' : Type u_6} [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 : Fintype ι] [inst_6 : Fintype ι'] [inst_7 : DecidableEq ι]
  [inst_8 : DecidableEq ι'] [inst_9 : Module.Free R M] [inst_10 : Module.Finite R M] (b : Module.Basis ι R L)
  (b' : Module.Basis ι' R L) (k : ℕ), (φ.polyCharpoly b).coeff k = 0 ↔ (φ.polyCharpoly b').coeff k = 0

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

1 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFintypeFintypeDecidableEqDecidableEqModule.FreeModule.Finite