Theorems · Definition · linear algebra

Subspace.quotDualEquivAnnihilator

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

The quotient by the dual is isomorphic to its dual annihilator.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleFiniteDimensional