Theorems · Definition · geometry

Affine.Simplex.orthogonalProjectionSpan

{𝕜 : Type u_1} →
  {V : Type u_2} →
    {P : Type u_3} →
      [inst : RCLike 𝕜] →
        [inst_1 : NormedAddCommGroup V] →
          [inst_2 : InnerProductSpace 𝕜 V] →
            [inst_3 : MetricSpace P] →
              [inst_4 : NormedAddTorsor V P] →
                {n : ℕ} → (s : Affine.Simplex 𝕜 P n) → P →ᴬ[𝕜] ↥(affineSpan 𝕜 (Set.range s.points))

The orthogonal projection of a point p onto the hyperplane spanned by the simplex's points.

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

33 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor