Theorems · Theorem · linear algebra

LinearMap.toMvPolynomial_baseChange

∀ {R : Type u_1} {M₁ : Type u_2} {M₂ : Type u_3} {ι₁ : Type u_4} {ι₂ : Type u_5} [inst : CommRing R]
  [inst_1 : AddCommGroup M₁] [inst_2 : AddCommGroup M₂] [inst_3 : Module R M₁] [inst_4 : Module R M₂]
  [inst_5 : Fintype ι₁] [inst_6 : Finite ι₂] [inst_7 : DecidableEq ι₁] (b₁ : Module.Basis ι₁ R M₁)
  (b₂ : Module.Basis ι₂ R M₂) (f : M₁ →ₗ[R] M₂) (i : ι₂) (A : Type u_6) [inst_8 : CommRing A] [inst_9 : Algebra R A],
  LinearMap.toMvPolynomial (Algebra.TensorProduct.basis A b₁) (Algebra.TensorProduct.basis A b₂)
      (LinearMap.baseChange A f) i =
    (MvPolynomial.map (algebraMap R A)) (LinearMap.toMvPolynomial b₁ b₂ f i)

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleFintypeFiniteDecidableEqCommRingAlgebra