Theorems · Theorem · geometry

finrank_vectorSpan_range_le

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} {ι : Type u_4} [inst : DivisionRing k] [inst_1 : AddCommGroup V]
  [inst_2 : Module k V] [inst_3 : AddTorsor V P] [inst_4 : Fintype ι] (p : ι → P) {n : ℕ},
  Fintype.card ι = n + 1 → Module.finrank k ↥(vectorSpan k (Set.range p)) ≤ n

The vectorSpan of an indexed family of n + 1 points has dimension at most n.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

2 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModuleAddTorsorFintype