Theorems · Definition · geometry

EuclideanGeometry.orthogonalProjection

{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] →
                (s : AffineSubspace 𝕜 P) → [inst_5 : Nonempty ↥s] → [s.direction.HasOrthogonalProjection] → P →ᴬ[𝕜] ↥s

The orthogonal projection of a point onto a nonempty affine subspace.

Defined in

Mathlib.Geometry.Euclidean.Projection

Cited by

85 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection