Theorems · Definition · linear algebra

LinearMap.domRestrict

{R : Type u_1} →
  {R₂ : Type u_3} →
    {M : Type u_5} →
      {M₂ : Type u_7} →
        [inst : Semiring R] →
          [inst_1 : Semiring R₂] →
            [inst_2 : AddCommMonoid M] →
              [inst_3 : AddCommMonoid M₂] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R₂ M₂] → {σ₁₂ : R →+* R₂} → (M →ₛₗ[σ₁₂] M₂) → (p : Submodule R M) → ↥p →ₛₗ[σ₁₂] M₂

The restriction of a linear map f : M → M₂ to a submodule p ⊆ M gives a linear map p → M₂.

Defined in

Mathlib.Algebra.Module.Submodule.LinearMap

Cited by

45 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule