Theorems · Theorem · linear algebra

LinearIndependent.group_smul

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {G : Type u_6} [hG : Group G] [inst_3 : MulAction G R] [inst_4 : SMul G M] [IsScalarTower G R M] [SMulCommClass G R M]
  {v : ι → M}, LinearIndependent R v → ∀ (w : ι → G), LinearIndependent R (w • v)

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleGroupMulActionSMulIsScalarTowerSMulCommClass