Theorems · Inductive type · functional analysis

Submodule.HasOrthogonalProjection

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] → [inst_1 : NormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → Submodule 𝕜 E → Prop

A subspace K : Submodule 𝕜 E has an orthogonal projection if every vector v : E admits an orthogonal projection to K.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

245 results in Mathlib

Foundations

Depth 46 from the axioms, rests on 429 definitions · uses propext, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace