Theorems · Theorem · linear algebra

linearIndepOn_finset_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} {s : Finset ι}, LinearIndepOn R v ↑s ↔ ∀ (f : ι → R), ∑ i ∈ s, f i • v i = 0 → ∀ i ∈ s, f i = 0

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

4 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModule