Theorems · Definition · functional analysis

Submodule.starProjection

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

The orthogonal projection onto a subspace as a map from the full space to itself, as opposed to Submodule.orthogonalProjectionOnto, which maps into the subtype. This version is important as it satisfies IsStarProjection.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

92 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection