Theorems · Definition · linear algebra

Module.Basis.extend

{K : Type u_3} →
  {V : Type u_4} →
    [inst : DivisionRing K] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module K V] → {s : Set V} → (hs : LinearIndepOn K id s) → Module.Basis (↑(hs.extend ⋯)) K V

If s is a linear independent set of vectors, we can extend it to a basis.

Defined in

Mathlib.LinearAlgebra.Basis.VectorSpace

Cited by

9 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule