Theorems · Theorem · linear algebra

linearIndependent_unique_iff

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} [inst : Ring R] [IsDomain R] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [Module.IsTorsionFree R M] {v : ι → M} [inst_5 : Unique ι],
  LinearIndependent R v ↔ v default ≠ 0

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Basic

Cited by

3 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingIsDomainAddCommGroupModuleModule.IsTorsionFreeUnique