Theorems · Definition · linear algebra

Submodule.dualRestrict

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → (W : Submodule R M) → Module.Dual R M →ₗ[R] Module.Dual R ↥W

The dualRestrict of a submodule W of M is the linear map from the dual of M to the dual of W such that the domain of each linear map is restricted to W.

Defined in

Mathlib.LinearAlgebra.Dual.Defs

Cited by

8 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModule