Theorems · Theorem · linear algebra

rank_span

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type w}
  [StrongRankCondition R] {v : ι → M},
  LinearIndependent R v → Module.rank R ↥(Submodule.span R (Set.range v)) = Cardinal.mk ↑(Set.range v)

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

6 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleStrongRankCondition