Theorems · Theorem · linear algebra

LinearMap.toMvPolynomial_comp

∀ {R : Type u_1} {M₁ : Type u_2} {M₂ : Type u_3} {M₃ : Type u_4} {ι₁ : Type u_5} {ι₂ : Type u_6} {ι₃ : Type u_7}
  [inst : CommRing R] [inst_1 : AddCommGroup M₁] [inst_2 : AddCommGroup M₂] [inst_3 : AddCommGroup M₃]
  [inst_4 : Module R M₁] [inst_5 : Module R M₂] [inst_6 : Module R M₃] [inst_7 : Fintype ι₁] [inst_8 : Fintype ι₂]
  [inst_9 : Finite ι₃] [inst_10 : DecidableEq ι₁] [inst_11 : DecidableEq ι₂] (b₁ : Module.Basis ι₁ R M₁)
  (b₂ : Module.Basis ι₂ R M₂) (b₃ : Module.Basis ι₃ R M₃) (g : M₂ →ₗ[R] M₃) (f : M₁ →ₗ[R] M₂) (i : ι₃),
  LinearMap.toMvPolynomial b₁ b₃ (g ∘ₗ f) i =
    (MvPolynomial.bind₁ (LinearMap.toMvPolynomial b₁ b₂ f)) (LinearMap.toMvPolynomial b₂ b₃ g i)

Defined in

Mathlib.Algebra.Module.LinearMap.Polynomial

Cited by

2 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupAddCommGroupModuleModuleModuleFintypeFintypeFiniteDecidableEqDecidableEq