Theorems · Definition · linear algebra

Subspace.quotAnnihilatorEquiv

{K : Type u_1} →
  {V : Type u_2} →
    [inst : Field K] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module K V] →
          (W : Subspace K V) → (Module.Dual K V ⧸ Submodule.dualAnnihilator W) ≃ₗ[K] Module.Dual K ↥W

The quotient by the dualAnnihilator of a subspace is isomorphic to the dual of that subspace.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModule