Theorems · Definition · linear algebra

MultilinearMap.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)] →
                        MultilinearMap R M₁' M₂ → ((i : ι) → M₁ i →ₗ[R] M₁' i) → MultilinearMap R M₁ M₂

If g is a multilinear map and f is a collection of linear maps, then g (f₁ m₁, ..., fₙ mₙ) is again a multilinear map, that we call g.compLinearMap f.

Defined in

Mathlib.LinearAlgebra.Multilinear.Basic

Cited by

26 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleAddCommMonoidModule