Theorems · Theorem · functional analysis

Submodule.orthogonalDecomposition_apply

∀ {𝕜 : Type u_1} {E : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  (K : Submodule 𝕜 E) [inst_3 : K.HasOrthogonalProjection] (x : E),
  K.orthogonalDecomposition x = WithLp.toLp 2 (K.orthogonalProjectionOnto x, Kᗮ.orthogonalProjectionOnto x)

Defined in

Mathlib.Analysis.InnerProductSpace.ProdL2

Cited by

6 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection