Theorems · Theorem · linear algebra

linearIndependent_iff_eq_zero_of_smul_mem_span

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {v : ι → M}, LinearIndependent R v ↔ ∀ (i : ι) (a : R), a • v i ∈ Submodule.span R (v '' (Set.univ \ {i})) → a = 0

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModule