Theorems · Definition · linear algebra

Module.Basis.toDualEquiv

{R : Type uR} →
  {M : Type uM} →
    {ι : Type uι} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] → [DecidableEq ι] → Module.Basis ι R M → [Finite ι] → M ≃ₗ[R] Module.Dual R M

A vector space is linearly equivalent to its dual space.

Defined in

Mathlib.LinearAlgebra.Dual.Basis

Cited by

9 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqFinite