Theorems · Theorem · linear algebra

MultilinearMap.zero_compLinearMap

∀ {R : Type uR} {ι : Type uι} {M₁ : ι → Type v₁} {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] [inst_5 : (i : ι) → AddCommMonoid (M₁' i)] [inst_6 : (i : ι) → Module R (M₁' i)]
  (f : (i : ι) → M₁ i →ₗ[R] M₁' i), MultilinearMap.compLinearMap 0 f = 0

Composing the zero multilinear map with a linear map in each argument.

Defined in

Mathlib.LinearAlgebra.Multilinear.Basic

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleAddCommMonoidModule