Theorems · Theorem · linear algebra

linearIndependent_algebraMap_comp_iff

∀ {ι : Type u_1} {ι' : Type u_2} [Finite ι'] {R : Type u_3} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : Algebra R S] [FaithfulSMul R S] [IsDomain S] {v : ι → ι' → R},
  (LinearIndependent S fun i => ⇑(algebraMap R S) ∘ v i) ↔ LinearIndependent R v

Defined in

Mathlib.LinearAlgebra.LinearIndependent.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteCommRingCommRingAlgebraFaithfulSMulIsDomain