add_compMultilinearMap — Mathlib

English

If S acts on the codomain, then (s • g) ∘ f = s • (g ∘ f) for a scalar action s on the linear map g.

Русский

Если S действует на кодомаппинг, то (s • g) ∘ f = s • (g ∘ f).

LaTeX

$$$$ (s \cdot g) .compMultilinearMap f = s . (g .compMultilinearMap f). $$$$

Lean4

@[simp]
theorem add_compMultilinearMap (g₁ g₂ : M₂ →ₗ[R] M₃) (f : MultilinearMap R M₁ M₂) :
    (g₁ + g₂).compMultilinearMap f = g₁.compMultilinearMap f + g₂.compMultilinearMap f :=
  rfl

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