Theorems · Definition · linear algebra

LinearIndepOn.extend

{ι : Type u'} →
  {K : Type u_3} →
    {V : Type u} →
      [inst : DivisionRing K] →
        [inst_1 : AddCommGroup V] →
          [inst_2 : Module K V] → {v : ι → V} → {s t : Set ι} → LinearIndepOn K v s → s ⊆ t → Set ι

LinearIndepOn.extend adds vectors to a linear independent set s ⊆ t until it spans all elements of t.

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Lemmas

Cited by

28 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule