Theorems · Theorem · linear algebra

LinearMap.polyCharpoly_baseChange

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} {ι : Type u_5} [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 : DecidableEq ι] [inst_7 : Module.Free R M] [inst_8 : Module.Finite R M]
  (b : Module.Basis ι R L) (A : Type u_8) [inst_9 : CommRing A] [inst_10 : Algebra R A],
  (LinearMap.tensorProduct R A M M ∘ₗ LinearMap.baseChange A φ).polyCharpoly (Algebra.TensorProduct.basis A b) =
    Polynomial.map (MvPolynomial.map (algebraMap R A)) (φ.polyCharpoly b)

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

0 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFintypeDecidableEqModule.FreeModule.FiniteCommRingAlgebra