Theorems · Definition · linear algebra

FiniteDimensional.basisSingleton

{K : Type u} →
  {V : Type v} →
    [inst : DivisionRing K] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module K V] →
          (ι : Type u_1) → [Unique ι] → Module.finrank K V = 1 → (v : V) → v ≠ 0 → Module.Basis ι K V

In a vector space with dimension 1, each set {v} is a basis for v ≠ 0.

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Basic

Cited by

7 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleUnique