Theorems · Theorem · functional analysis

Submodule.starProjection_singleton

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {v : E} (w : E), (𝕜 ∙ v).starProjection w = (inner 𝕜 v w / ↑(‖v‖ ^ 2)) • v

Formula for orthogonal projection onto a single vector.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

4 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace