smulRight — Mathlib

English

For an f: M1 → M2 valued in R, and z in M2, the map f.smulRight z satisfies (f s m) = f(m) · z.

Русский

Для f: M1 → M2 значимого в R и z ∈ M2, f.smulRight z удовлетворяет f.smulRight z (m) = f(m) · z.

LaTeX

$$$$f.smulRight(z)(m) = f(m) \cdot z.$$$$

Lean4

/-- Given an `R`-multilinear map `f` taking values in `R`, `f.smulRight z` is the map
sending `m` to `f m • z`. -/
def smulRight (f : MultilinearMap R M₁ R) (z : M₂) : MultilinearMap R M₁ M₂ :=
  (LinearMap.smulRight LinearMap.id z).compMultilinearMap f

Похожие утверждения