Theorems · Theorem · linear algebra

MultilinearMap.map_update_smul

∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {M₂ : Type v₂} [inst : Semiring 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] (m : (i : ι) → M₁ i) (i : ι) (c : R)
  (x : M₁ i), f (Function.update m i (c • x)) = c • f (Function.update m i x)

Earlier, this name was used by what is now called MultilinearMap.map_update_smul_left.

Defined in

Mathlib.LinearAlgebra.Multilinear.Basic

Cited by

8 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleDecidableEq