Theorems · Theorem · functional analysis

Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff

Deprecated since 2026-05-05Use Submodule.orthogonalProjectionOnto_comp_subtypeL_eq_zero_iff instead.

∀ {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.orthogonalProjectionOnto ∘SL V.subtypeL = 0 ↔ U ⟂ V

Alias of Submodule.orthogonalProjectionOnto_comp_subtypeL_eq_zero_iff. The projection into U from V is the zero map if and only if U and V are orthogonal.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

0 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection