Theorems · Definition · functional analysis

Submodule.orthogonalProjectionOnto

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : InnerProductSpace 𝕜 E] → (K : Submodule 𝕜 E) → [K.HasOrthogonalProjection] → E →L[𝕜] ↥K

The orthogonal projection onto a subspace.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

103 results in Mathlib

Foundations

Depth 175 from the axioms, rests on 4,230 definitions · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection