Theorems · Theorem · functional analysis

Submodule.starProjection_comp_starProjection_eq_zero_iff

∀ {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] [inst_4 : V.HasOrthogonalProjection],
  U.starProjection ∘SL V.starProjection = 0 ↔ U ⟂ V

U.starProjection ∘ V.starProjection = 0 iff U and V are pairwise 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.HasOrthogonalProjectionSubmodule.HasOrthogonalProjection