Theorems · Definition · linear algebra

Module.Basis.ofSpan

{K : Type u_3} →
  {V : Type u_4} →
    [inst : DivisionRing K] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module K V] → {s : Set V} → ⊤ ≤ Submodule.span K s → Module.Basis (↑(⋯.extend ⋯)) K V

If a set s spans the space, this is a basis contained in s.

Defined in

Mathlib.LinearAlgebra.Basis.VectorSpace

Cited by

4 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule