Theorems · Definition · linear algebra

Module.Basis.span

{ι : Type u_1} →
  {R : Type u_3} →
    {M : Type u_5} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            {v : ι → M} → LinearIndependent R v → Module.Basis ι R ↥(Submodule.span R (Set.range v))

A linear independent family of vectors is a basis for their span.

Defined in

Mathlib.LinearAlgebra.Basis.Basic

Cited by

11 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule