Theorems · Theorem · linear algebra

LinearIndependent.comp

∀ {ι : Type u'} {ι' : Type u_1} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M], LinearIndependent R v → ∀ (f : ι' → ι), Function.Injective f → LinearIndependent R (v ∘ f)

A subfamily of a linearly independent family (i.e., a composition with an injective map) is a linearly independent family.

Defined in

Mathlib.LinearAlgebra.LinearIndependent.Defs

Cited by

41 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule