Base change for linear independence

This file is a place to collect base change results for linear independence.

@[simp]

theorem linearIndependent_algebraMap_comp_iff {ι : Type u_1} {ι' : Type u_2} [Finite ι'] {R : Type u_3} {S : Type u_4} [CommRing R] [CommRing S] [Algebra R S] [FaithfulSMul R S] [IsDomain S] {v : ι → ι' → R} : (LinearIndependent S fun (i : ι) => ⇑(algebraMap R S) ∘ v i) ↔ LinearIndependent R v