Theorems · Theorem · linear algebra

linearIndependent_iff_injective_fintypeLinearCombination

∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : Fintype ι],
  LinearIndependent R v ↔ Function.Injective ⇑(Fintype.linearCombination R v)

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

3 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleFintype