Theorems · Theorem · linear algebra

MultilinearMap.map_update_smul_left

∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {M₂ : Type v₂} [inst : CommSemiring R]
  [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : AddCommMonoid M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
  [inst_4 : Module R M₂] (f : MultilinearMap R M₁ M₂) [inst_5 : DecidableEq ι] [inst_6 : Fintype ι] (m : (i : ι) → M₁ i)
  (i : ι) (c : R) (x : M₁ i), f (Function.update (c • m) i x) = c ^ (Fintype.card ι - 1) • f (Function.update m i x)

Defined in

Mathlib.LinearAlgebra.Multilinear.Basic

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleDecidableEqFintype