Theorems · Definition · linear algebra

Subspace.orderIsoFiniteDimensional

{K : Type u_4} →
  {V : Type u_5} →
    [inst : Field K] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module K V] → [FiniteDimensional K V] → Subspace K V ≃o (Subspace K (Module.Dual K V))ᵒᵈ

For any finite-dimensional vector space, dualAnnihilator and dualCoannihilator give an antitone order isomorphism between the subspaces in the vector space and the subspaces in its dual.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleFiniteDimensional