Theorems · Theorem · linear algebra

linearIndependent_iff_notMem_span

∀ {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}, LinearIndependent K v ↔ ∀ (i : ι), v i ∉ Submodule.span K (v '' (Set.univ \ {i}))

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule