Theorems · Theorem · linear algebra

linearIndependent_sum

∀ {ι : Type u'} {ι' : Type u_1} {R : Type u_2} {M : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] {v : ι ⊕ ι' → M},
  LinearIndependent R v ↔
    LinearIndependent R (v ∘ Sum.inl) ∧
      LinearIndependent R (v ∘ Sum.inr) ∧
        Disjoint (Submodule.span R (Set.range (v ∘ Sum.inl))) (Submodule.span R (Set.range (v ∘ Sum.inr)))

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModule