Theorems · Theorem · geometry

Projectivization.dependent_iff

∀ {ι : Type u_1} {K : Type u_2} {V : Type u_3} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  {f : ι → Projectivization K V}, Projectivization.Dependent f ↔ ¬LinearIndependent K (Projectivization.rep ∘ f)

A family of points in a projective space is dependent if and only if their representatives are linearly dependent.

Defined in

Mathlib.LinearAlgebra.Projectivization.Independence

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule