Theorems · Theorem · functional analysis

Submodule.inner_orthogonalProjectionOnto_eq_of_mem_left

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {K : Submodule 𝕜 E} [inst_3 : K.HasOrthogonalProjection] (u : ↥K) (v : E),
  inner 𝕜 u (K.orthogonalProjectionOnto v) = inner 𝕜 (↑u) v

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

4 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection