linearHom — Mathlib

English

The affine map prodMap takes f : P1 →ᵃ[k] P2 and g : P3 →ᵃ[k] P4 to a map P1 × P3 →ᵃ[k] P2 × P4 with toFun = Prod.map f g and linear = f.linear.prodMap g.linear.

Русский

Аффинное отображение prodMap принимает f : P1 →ᵃ P2 и g : P3 →ᵃ P4 и возвращает отображение P1 × P3 →ᵃ P2 × P4 с toFun = Prod.map f g и линейной частью = f.linear.prodMap g.linear.

LaTeX

$$$\\mathrm{prodMap}(f,g) : P_1 \\times P_3 \\to^a_k P_2 \\times P_4$ with toFun = \\mathrm{Prod.map}(f,g) and linear = f.linear.prodMap g.linear$$$

Lean4

/-- `AffineMap.linear` on endomorphisms is a `MonoidHom`. -/
@[simps]
def linearHom : (P1 →ᵃ[k] P1) →* V1 →ₗ[k] V1 where
  toFun := linear
  map_one' := rfl
  map_mul' _ _ := rfl

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