toLinearMap — Mathlib

English

If f' is surjective, then for every n, f'^n is surjective.

Русский

Если f' сюръективен, то для каждого n сюръективно f'^n.

LaTeX

$$$\\forall n,\\; \\text{Surjective}(f'^n).$$$

Lean4

/-- Each element of the monoid defines a linear map.

This is a stronger version of `DistribMulAction.toAddMonoidHom`. -/
@[simps]
def toLinearMap (s : S) : M →ₗ[R] M where
  toFun := HSMul.hSMul s
  map_add' := smul_add s
  map_smul' _ _ := smul_comm _ _ _

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