Theorems · Theorem · functional analysis

Submodule.IsOrtho.orthogonalProjectionOnto_comp_subtypeL

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {U V : Submodule 𝕜 E} [inst_3 : U.HasOrthogonalProjection], U ⟂ V → U.orthogonalProjectionOnto ∘SL V.subtypeL = 0

The projection into U from an orthogonal submodule V is the zero map.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

3 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection