Theorems · Theorem · linear algebra

Fintype.linearIndependent_iff

∀ {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} [inst_3 : Fintype ι], LinearIndependent R v ↔ ∀ (g : ι → R), ∑ i, g i • v i = 0 → ∀ (i : ι), g i = 0

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

17 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleFintype