Theorems · Theorem · linear algebra

FiniteDimensional.range_basisSingleton

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] (ι : Type u_1)
  [inst_3 : Unique ι] (h : Module.finrank K V = 1) (v : V) (hv : v ≠ 0),
  Set.range ⇑(FiniteDimensional.basisSingleton ι h v hv) = {v}

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Basic

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleUnique