Theorems · Definition · linear algebra

Module.DualBases.basis

{R : Type u_1} →
  {M : Type u_2} →
    {ι : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] → {e : ι → M} → {ε : ι → Module.Dual R M} → Module.DualBases e ε → Module.Basis ι R M

(h : DualBases e ε).basis shows the family of vectors e forms a basis.

Defined in

Mathlib.LinearAlgebra.Dual.Basis

Cited by

5 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule