Theorems · Theorem · geometry

vectorSpan_range_eq_span_range_vsub_right

∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} (p : ι → P) (i0 : ι),
  vectorSpan k (Set.range p) = Submodule.span k (Set.range fun i => p i -ᵥ p i0)

The vectorSpan of an indexed family is the span of the pairwise subtractions with a given point on the right.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor