Theorems · Definition · linear algebra

LinearEquiv.flip

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : AddCommGroup M] →
          [inst_2 : Module R M] →
            [inst_3 : AddCommGroup N] →
              [inst_4 : Module R N] → [Module.IsReflexive R M] → (N ≃ₗ[R] Module.Dual R M) → M ≃ₗ[R] Module.Dual R N

For a reflexive module M, an equivalence N ≃ₗ[R] Dual R M naturally yields an equivalence M ≃ₗ[R] Dual R N. Such equivalences are known as perfect pairings.

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Basic

Cited by

10 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleModule.IsReflexive