Theorems · Theorem · linear algebra

LinearMap.polyCharpolyAux_map_eval

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} {ι : Type u_5} {ιM : Type u_7} [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 ιM] [inst_7 : DecidableEq ι]
  [inst_8 : DecidableEq ιM] (b : Module.Basis ι R L) (bₘ : Module.Basis ιM R M) [inst_9 : Module.Finite R M]
  [inst_10 : Module.Free R M] (x : ι → R),
  Polynomial.map (MvPolynomial.eval x) (φ.polyCharpolyAux b bₘ) =
    LinearMap.charpoly (φ (b.repr.symm (Finsupp.equivFunOnFinite.symm x)))

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

1 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFintypeFintypeDecidableEqDecidableEqModule.FiniteModule.Free